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Lp Square Function Estimates On Spaces Of Homogeneous Type And On Uniformly Rectifiable Sets
Download Lp Square Function Estimates On Spaces Of Homogeneous Type And On Uniformly Rectifiable Sets full books in PDF, epub, and Kindle. Read online Lp Square Function Estimates On Spaces Of Homogeneous Type And On Uniformly Rectifiable Sets ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis $L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets by : Steve Hofmann
Download or read book $L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets written by Steve Hofmann and published by American Mathematical Soc.. This book was released on 2017-01-18 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, they consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The local theorem is then used to establish an inductive scheme in which square function estimates on so-called big pieces of an Ahlfors-David regular set are proved to be sufficient for square function estimates to hold on the entire set. Extrapolation results for and Hardy space versions of these estimates are also established. Moreover, the authors prove square function estimates for integral operators associated with variable coefficient kernels, including the Schwartz kernels of pseudodifferential operators acting between vector bundles on subdomains with uniformly rectifiable boundaries on manifolds.
Book Synopsis Lp-square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets by : Steve Hofmann
Download or read book Lp-square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets written by Steve Hofmann and published by . This book was released on 2017 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Hodge-Laplacian by : Dorina Mitrea
Download or read book The Hodge-Laplacian written by Dorina Mitrea and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-10-10 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and relative boundary conditions for differential forms, this monograph treats the Hodge-Laplacian equipped with classical Dirichlet, Neumann, Transmission, Poincaré, and Robin boundary conditions in regular Semmes-Kenig-Toro domains. Lying at the intersection of partial differential equations, harmonic analysis, and differential geometry, this text is suitable for a wide range of PhD students, researchers, and professionals. Contents: Preface Introduction and Statement of Main Results Geometric Concepts and Tools Harmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR Domains Harmonic Layer Potentials Associated with the Levi-Civita Connection on UR Domains Dirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT Domains Fatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT Domains Solvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham Formalism Additional Results and Applications Further Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford Analysis Bibliography Index
Book Synopsis Multi-Layer Potentials and Boundary Problems by : Irina Mitrea
Download or read book Multi-Layer Potentials and Boundary Problems written by Irina Mitrea and published by Springer. This book was released on 2013-01-05 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. When the differential operator under discussion is of second order a variety of tools are available for dealing with such problems, including boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis. When the differential operator is of higher-order (as is the case, e.g., with anisotropic plate bending when one deals with a fourth order operator) only a few options could be successfully implemented. In the 1970s Alberto Calderón, one of the founders of the modern theory of Singular Integral Operators, advocated the use of layer potentials for the treatment of higher-order elliptic boundary value problems. The present monograph represents the first systematic treatment based on this approach. This research monograph lays, for the first time, the mathematical foundation aimed at solving boundary value problems for higher-order elliptic operators in non-smooth domains using the layer potential method and addresses a comprehensive range of topics, dealing with elliptic boundary value problems in non-smooth domains including layer potentials, jump relations, non-tangential maximal function estimates, multi-traces and extensions, boundary value problems with data in Whitney–Lebesque spaces, Whitney–Besov spaces, Whitney–Sobolev- based Lebesgue spaces, Whitney–Triebel–Lizorkin spaces,Whitney–Sobolev-based Hardy spaces, Whitney–BMO and Whitney–VMO spaces.
Book Synopsis Geometric Harmonic Analysis III by : Dorina Mitrea
Download or read book Geometric Harmonic Analysis III written by Dorina Mitrea and published by Springer Nature. This book was released on 2023-05-12 with total page 980 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. Volume III is concerned with integral representation formulas for nullsolutions of elliptic PDEs, Calderón-Zygmund theory for singular integral operators, Fatou type theorems for systems of elliptic PDEs, and applications to acoustic and electromagnetic scattering. Overall, this amounts to a powerful and nuanced theory developed on uniformly rectifiable sets, which builds on the work of many predecessors.
Book Synopsis Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory by : H. Hofer
Download or read book Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory written by H. Hofer and published by American Mathematical Soc.. This book was released on 2017-07-13 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors start with the construction of the symplectic field theory (SFT). As a general theory of symplectic invariants, SFT has been outlined in Introduction to symplectic field theory (2000), by Y. Eliashberg, A. Givental and H. Hofer who have predicted its formal properties. The actual construction of SFT is a hard analytical problem which will be overcome be means of the polyfold theory due to the present authors. The current paper addresses a significant amount of the arising issues and the general theory will be completed in part II of this paper. To illustrate the polyfold theory the authors use the results of the present paper to describe an alternative construction of the Gromov-Witten invariants for general compact symplectic manifolds.
Book Synopsis Weighted Morrey Spaces by : Marcus Laurel
Download or read book Weighted Morrey Spaces written by Marcus Laurel and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-09-02 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a testament to the potency of the method of singular integrals of layer potential type in solving boundary value problems for weakly elliptic systems in the setting of Muckenhoupt-weighted Morrey spaces and their pre-duals. A functional analytic framework for Muckenhoupt-weighted Morrey spaces in the rough setting of Ahlfors regular sets is built from the ground up and subsequently supports a Calderón-Zygmund theory on this brand of Morrey space in the optimal geometric environment of uniformly rectifiable sets. A thorough duality theory for such Morrey spaces is also developed and ushers in a never-before-seen Calderón-Zygmund theory for Muckenhoupt-weighted Block spaces. Both weighted Morrey and Block spaces are also considered through the lens of (generalized) Banach function spaces, and ultimately, a variety of boundary value problems are formulated and solved with boundary data arbitrarily prescribed from either scale of space. The fairly self-contained nature of this monograph ensures that graduate students, researchers, and professionals in a variety of fields, e.g., function space theory, harmonic analysis, and PDE, will find this monograph a welcome and valuable addition to the mathematical literature.
Book Synopsis Rationality Problem for Algebraic Tori by : Akinari Hoshi
Download or read book Rationality Problem for Algebraic Tori written by Akinari Hoshi and published by American Mathematical Soc.. This book was released on 2017-07-13 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give the complete stably rational classification of algebraic tori of dimensions and over a field . In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank and is given. The authors show that there exist exactly (resp. , resp. ) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension , and there exist exactly (resp. , resp. ) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension . The authors make a procedure to compute a flabby resolution of a -lattice effectively by using the computer algebra system GAP. Some algorithms may determine whether the flabby class of a -lattice is invertible (resp. zero) or not. Using the algorithms, the suthors determine all the flabby and coflabby -lattices of rank up to and verify that they are stably permutation. The authors also show that the Krull-Schmidt theorem for -lattices holds when the rank , and fails when the rank is ...
Book Synopsis Special Values of the Hypergeometric Series by : Akihito Ebisu
Download or read book Special Values of the Hypergeometric Series written by Akihito Ebisu and published by American Mathematical Soc.. This book was released on 2017-07-13 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the author presents a new method for finding identities for hypergeoemtric series, such as the (Gauss) hypergeometric series, the generalized hypergeometric series and the Appell-Lauricella hypergeometric series. Furthermore, using this method, the author gets identities for the hypergeometric series and shows that values of at some points can be expressed in terms of gamma functions, together with certain elementary functions. The author tabulates the values of that can be obtained with this method and finds that this set includes almost all previously known values and many previously unknown values.
Book Synopsis Absolute Continuity Under Time Shift of Trajectories and Related Stochastic Calculus by : Jörg-Uwe Löbus
Download or read book Absolute Continuity Under Time Shift of Trajectories and Related Stochastic Calculus written by Jörg-Uwe Löbus and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text is concerned with a class of two-sided stochastic processes of the form . Here is a two-sided Brownian motion with random initial data at time zero and is a function of . Elements of the related stochastic calculus are introduced. In particular, the calculus is adjusted to the case when is a jump process. Absolute continuity of under time shift of trajectories is investigated. For example under various conditions on the initial density with respect to the Lebesgue measure, , and on with we verify i.e. where the product is taken over all coordinates. Here is the divergence of with respect to the initial position. Crucial for this is the temporal homogeneity of in the sense that , , where is the trajectory taking the constant value . By means of such a density, partial integration relative to a generator type operator of the process is established. Relative compactness of sequences of such processes is established.
Book Synopsis Geometric Harmonic Analysis II by : Dorina Mitrea
Download or read book Geometric Harmonic Analysis II written by Dorina Mitrea and published by Springer Nature. This book was released on 2023-03-03 with total page 938 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is part of a larger program, materializing in five volumes, whose principal aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. Volume II is concerned with function spaces measuring size and/or smoothness, such as Hardy spaces, Besov spaces, Triebel-Lizorkin spaces, Sobolev spaces, Morrey spaces, Morrey-Campanato spaces, spaces of functions of Bounded Mean Oscillations, etc., in general geometric settings. Work here also highlights the close interplay between differentiability properties of functions and singular integral operators. The text is intended for researchers, graduate students, and industry professionals interested in harmonic analysis, functional analysis, geometric measure theory, and function space theory.
Book Synopsis Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems by : Igor Burban
Download or read book Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems written by Igor Burban and published by American Mathematical Soc.. This book was released on 2017-07-13 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article the authors develop a new method to deal with maximal Cohen–Macaulay modules over non–isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen–Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen–Macaulay representation type. The authors' approach is illustrated on the case of k as well as several other rings. This study of maximal Cohen–Macaulay modules over non–isolated singularities leads to a new class of problems of linear algebra, which the authors call representations of decorated bunches of chains. They prove that these matrix problems have tame representation type and describe the underlying canonical forms.
Book Synopsis Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem by : Denis R. Hirschfeldt
Download or read book Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem written by Denis R. Hirschfeldt and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Goncharov and Peretyat'kin independently gave necessary and sufficient conditions for when a set of types of a complete theory is the type spectrum of some homogeneous model of . Their result can be stated as a principle of second order arithmetic, which is called the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic Model Theorem (AMT), which states that every complete atomic theory has an atomic model. The authors show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense and do the same for an analogous result of Peretyat'kin giving necessary and sufficient conditions for when a set of types is the type spectrum of some model.
Book Synopsis Hypercontractivity in Group von Neumann Algebras by : Marius Junge
Download or read book Hypercontractivity in Group von Neumann Algebras written by Marius Junge and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the authors provide a combinatorial/numerical method to establish new hypercontractivity estimates in group von Neumann algebras. They illustrate their method with free groups, triangular groups and finite cyclic groups, for which they obtain optimal time hypercontractive inequalities with respect to the Markov process given by the word length and with an even integer. Interpolation and differentiation also yield general hypercontrativity for via logarithmic Sobolev inequalities. The authors' method admits further applications to other discrete groups without small loops as far as the numerical part—which varies from one group to another—is implemented and tested on a computer. The authors also develop another combinatorial method which does not rely on computational estimates and provides (non-optimal) hypercontractive inequalities for a larger class of groups/lengths, including any finitely generated group equipped with a conditionally negative word length, like infinite Coxeter groups. The authors' second method also yields hypercontractivity bounds for groups admitting a finite dimensional proper cocycle. Hypercontractivity fails for conditionally negative lengths in groups satisfying Kazhdan's property (T).
Book Synopsis On Operads, Bimodules and Analytic Functors by : Nicola Gambino
Download or read book On Operads, Bimodules and Analytic Functors written by Nicola Gambino and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop further the theory of operads and analytic functors. In particular, they introduce the bicategory of operad bimodules, that has operads as -cells, operad bimodules as -cells and operad bimodule maps as 2-cells, and prove that it is cartesian closed. In order to obtain this result, the authors extend the theory of distributors and the formal theory of monads.
Book Synopsis Needle Decompositions in Riemannian Geometry by : Bo’az Klartag
Download or read book Needle Decompositions in Riemannian Geometry written by Bo’az Klartag and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Book Synopsis Knot Invariants and Higher Representation Theory by : Ben Webster
Download or read book Knot Invariants and Higher Representation Theory written by Ben Webster and published by American Mathematical Soc.. This book was released on 2018-01-16 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for sl and sl and by Mazorchuk-Stroppel and Sussan for sl . The author's technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These are the representation categories of certain finite dimensional algebras with an explicit diagrammatic presentation, generalizing the cyclotomic quotient of the KLR algebra. When the Lie algebra under consideration is sl , the author shows that these categories agree with certain subcategories of parabolic category for gl .
