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Theory Of Fundamental Bessel Functions Of High Rank
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Book Synopsis Theory of Fundamental Bessel Functions of High Rank by : Zhi Qi
Download or read book Theory of Fundamental Bessel Functions of High Rank written by Zhi Qi and published by American Mathematical Society. This book was released on 2021-02-10 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, the author studies fundamental Bessel functions for $mathrm{GL}_n(mathbb F)$ arising from the Voronoí summation formula for any rank $n$ and field $mathbb F = mathbb R$ or $mathbb C$, with focus on developing their analytic and asymptotic theory. The main implements and subjects of this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.
Book Synopsis Resolvent, Heat Kernel, and Torsion under Degeneration to Fibered Cusps by : Pierre Albin
Download or read book Resolvent, Heat Kernel, and Torsion under Degeneration to Fibered Cusps written by Pierre Albin and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds with fibered cusps are a class of complete non-compact Riemannian manifolds including many examples of locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold undergoing degeneration to a manifold with fibered cusps. We obtain precise asymptotics for the resolvent, the heat kernel, and the determinant of the Laplacian. Using these asymptotics we obtain a topological description of the analytic torsion on a manifold with fibered cusps in terms of the R-torsion of the underlying manifold with boundary.
Book Synopsis Local Well-Posedness and Break-Down Criterion of the Incompressible Euler Equations with Free Boundary by : Chao Wang
Download or read book Local Well-Posedness and Break-Down Criterion of the Incompressible Euler Equations with Free Boundary written by Chao Wang and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we prove the local well-posedness of the free boundary problem for the incompressible Euler equations in low regularity Sobolev spaces, in which the velocity is a Lipschitz function and the free surface belongs to C 3 2 +ε. Moreover, we also present a Beale-Kato-Majda type break-down criterion of smooth solution in terms of the mean curvature of the free surface, the gradient of the velocity and Taylor sign condition.
Book Synopsis Paley-Wiener Theorems for a p-Adic Spherical Variety by : Patrick Delorme
Download or read book Paley-Wiener Theorems for a p-Adic Spherical Variety written by Patrick Delorme and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let SpXq be the Schwartz space of compactly supported smooth functions on the p-adic points of a spherical variety X, and let C pXq be the space of Harish-Chandra Schwartz functions. Under assumptions on the spherical variety, which are satisfied when it is symmetric, we prove Paley–Wiener theorems for the two spaces, characterizing them in terms of their spectral transforms. As a corollary, we get relative analogs of the smooth and tempered Bernstein centers — rings of multipliers for SpXq and C pXq.WhenX “ a reductive group, our theorem for C pXq specializes to the well-known theorem of Harish-Chandra, and our theorem for SpXq corresponds to a first step — enough to recover the structure of the Bern-stein center — towards the well-known theorems of Bernstein [Ber] and Heiermann [Hei01].
Book Synopsis Bounded Littlewood Identities by : Eric M. Rains
Download or read book Bounded Littlewood Identities written by Eric M. Rains and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe a method, based on the theory of Macdonald–Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald’s partial fraction technique and results in the first examples of bounded Littlewood identities for Macdonald polynomials. These identities, which take the form of decomposition formulas for Macdonald polynomials of type (R, S) in terms of ordinary Macdonald polynomials, are q, t-analogues of known branching formulas for characters of the symplectic, orthogonal and special orthogonal groups. In the classical limit, our method implies that MacMahon’s famous ex-conjecture for the generating function of symmetric plane partitions in a box follows from the identification of GL(n, R), O(n) as a Gelfand pair. As further applications, we obtain combinatorial formulas for characters of affine Lie algebras; Rogers–Ramanujan identities for affine Lie algebras, complementing recent results of Griffin et al.; and quadratic transformation formulas for Kaneko–Macdonald-type basic hypergeometric series.
Book Synopsis Linear Dynamical Systems on Hilbert Spaces: Typical Properties and Explicit Examples by : S. Grivaux
Download or read book Linear Dynamical Systems on Hilbert Spaces: Typical Properties and Explicit Examples written by S. Grivaux and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: We solve a number of questions pertaining to the dynamics of linear operators on Hilbert spaces, sometimes by using Baire category arguments and sometimes by constructing explicit examples. In particular, we prove the following results. (i) A typical hypercyclic operator is not topologically mixing, has no eigen-values and admits no non-trivial invariant measure, but is densely distri-butionally chaotic. (ii) A typical upper-triangular operator with coefficients of modulus 1 on the diagonal is ergodic in the Gaussian sense, whereas a typical operator of the form “diagonal with coefficients of modulus 1 on the diagonal plus backward unilateral weighted shift” is ergodic but has only countably many unimodular eigenvalues; in particular, it is ergodic but not ergodic in the Gaussian sense. (iii) There exist Hilbert space operators which are chaotic and U-frequently hypercyclic but not frequently hypercyclic, Hilbert space operators which are chaotic and frequently hypercyclic but not ergodic, and Hilbert space operators which are chaotic and topologically mixing but not U-frequently hypercyclic. We complement our results by investigating the descriptive complexity of some natural classes of operators defined by dynamical properties.
Book Synopsis Weakly Modular Graphs and Nonpositive Curvature by : Jérémie Chalopin
Download or read book Weakly Modular Graphs and Nonpositive Curvature written by Jérémie Chalopin and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article investigates structural, geometrical, and topological characteri-zations and properties of weakly modular graphs and of cell complexes derived from them. The unifying themes of our investigation are various “nonpositive cur-vature” and “local-to-global” properties and characterizations of weakly modular graphs and their subclasses. Weakly modular graphs have been introduced as a far-reaching common generalization of median graphs (and more generally, of mod-ular and orientable modular graphs), Helly graphs, bridged graphs, and dual polar graphs occurring under different disguises (1–skeletons, collinearity graphs, covering graphs, domains, etc.) in several seemingly-unrelated fields of mathematics: * Metric graph theory * Geometric group theory * Incidence geometries and buildings * Theoretical computer science and combinatorial optimization We give a local-to-global characterization of weakly modular graphs and their sub-classes in terms of simple connectedness of associated triangle-square complexes and specific local combinatorial conditions. In particular, we revisit characterizations of dual polar graphs by Cameron and by Brouwer-Cohen. We also show that (disk-)Helly graphs are precisely the clique-Helly graphs with simply connected clique complexes. With l1–embeddable weakly modular and sweakly modular graphs we associate high-dimensional cell complexes, having several strong topological and geometrical properties (contractibility and the CAT(0) property). Their cells have a specific structure: they are basis polyhedra of even –matroids in the first case and orthoscheme complexes of gated dual polar subgraphs in the second case. We resolve some open problems concerning subclasses of weakly modular graphs: we prove a Brady-McCammond conjecture about CAT(0) metric on the orthoscheme.
Book Synopsis The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners by : Paul Godin
Download or read book The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners written by Paul Godin and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study 2D compressible Euler flows in bounded impermeable domains whose boundary is smooth except for corners. We assume that the angles of the corners are small enough. Then we obtain local (in time) existence of solutions which keep the L2 Sobolev regularity of their Cauchy data, provided the external forces are sufficiently regular and suitable compatibility conditions are satisfied. Such a result is well known when there is no corner. Our proof relies on the study of associated linear problems. We also show that our results are rather sharp: we construct counterexamples in which the smallness condition on the angles is not fulfilled and which display a loss of L2 Sobolev regularity with respect to the Cauchy data and the external forces.
Book Synopsis The Yang-Mills Heat Equation with Finite Action in Three Dimensions by : Leonard Gross
Download or read book The Yang-Mills Heat Equation with Finite Action in Three Dimensions written by Leonard Gross and published by American Mathematical Society. This book was released on 2022-02-02 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Uniqueness of Fat-Tailed Self-Similar Profiles to Smoluchowski?s Coagulation Equation for a Perturbation of the Constant Kernel by : Sebastian Throm
Download or read book Uniqueness of Fat-Tailed Self-Similar Profiles to Smoluchowski?s Coagulation Equation for a Perturbation of the Constant Kernel written by Sebastian Throm and published by American Mathematical Society. This book was released on 2021-09-24 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities by : William Gignac
Download or read book Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities written by William Gignac and published by American Mathematical Society. This book was released on 2021-11-16 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Non-Kissing Complexes and Tau-Tilting for Gentle Algebras by : Yann Palu
Download or read book Non-Kissing Complexes and Tau-Tilting for Gentle Algebras written by Yann Palu and published by American Mathematical Society. This book was released on 2021-12-30 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups by : Pierre Patie
Download or read book Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups written by Pierre Patie and published by American Mathematical Society. This book was released on 2021-11-16 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Intense Automorphisms of Finite Groups by : Mima Stanojkovski
Download or read book Intense Automorphisms of Finite Groups written by Mima Stanojkovski and published by American Mathematical Society. This book was released on 2021-12-09 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs by : Stefan Geiss
Download or read book Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs written by Stefan Geiss and published by American Mathematical Society. This book was released on 2021-11-16 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Naturality and Mapping Class Groups in Heegard Floer Homology by : András Juhász
Download or read book Naturality and Mapping Class Groups in Heegard Floer Homology written by András Juhász and published by American Mathematical Society. This book was released on 2021-12-09 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Ergodicity of Markov Processes via Nonstandard Analysis by : Haosui Duanmu
Download or read book Ergodicity of Markov Processes via Nonstandard Analysis written by Haosui Duanmu and published by American Mathematical Society. This book was released on 2021-12-09 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
