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Weighted Shifts On Directed Trees
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Book Synopsis Weighted Shifts on Directed Trees by : Zenon Jan Jablónski
Download or read book Weighted Shifts on Directed Trees written by Zenon Jan Jablónski and published by American Mathematical Soc.. This book was released on 2012 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new class of (not necessarily bounded) operators related to (mainly infinite) directed trees is introduced and investigated. Operators in question are to be considered as a generalization of classical weighted shifts, on the one hand, and of weighted adjacency operators, on the other; they are called weighted shifts on directed trees. The basic properties of such operators, including closedness, adjoints, polar decomposition and moduli are studied. Circularity and the Fredholmness of weighted shifts on directed trees are discussed. The relationships between domains of a weighted shift on a directed tree and its adjoint are described. Hyponormality, cohyponormality, subnormality and complete hyperexpansivity of such operators are entirely characterized in terms of their weights. Related questions that arose during the study of the topic are solved as well.
Book Synopsis Handbook of Analytic Operator Theory by : Kehe Zhu
Download or read book Handbook of Analytic Operator Theory written by Kehe Zhu and published by CRC Press. This book was released on 2019-05-10 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Analytic Operator Theory thoroughly covers the subject of holomorphic function spaces and operators acting on them. The spaces covered include Bergman spaces, Hardy spaces, Fock spaces and the Drury-Averson space. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class operators. The volume consists of eleven articles in the general area of analytic function spaces and operators on them. Each contributor focuses on one particular topic, for example, operator theory on the Drury-Aversson space, and presents the material in the form of a survey paper which contains all the major results in the area and includes all relevant references. The overalp between this volume and existing books in the area is minimal. The material on two-variable weighted shifts by Curto, the Drury-Averson space by Fang and Xia, the Cowen-Douglas class by Misra, and operator theory on the bi-disk by Yang has never appeared in book form before. Features: The editor of the handbook is a widely known and published researcher on this topic The handbook's contributors are a who's=who of top researchers in the area The first contributed volume on these diverse topics
Book Synopsis Unbounded Weighted Composition Operators in L2-Spaces by : Piotr Budzyński
Download or read book Unbounded Weighted Composition Operators in L2-Spaces written by Piotr Budzyński and published by Springer. This book was released on 2018-05-28 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book establishes the foundations of the theory of bounded and unbounded weighted composition operators in L2-spaces. It develops the theory in full generality, meaning that the corresponding composition operators are not assumed to be well defined. A variety of seminormality properties of unbounded weighted composition operators are characterized. The first-ever criteria for subnormality of unbounded weighted composition operators are provided and the subtle interplay between the classical moment problem, graph theory and the injectivity problem for weighted composition operators is revealed. The relationships between weighted composition operators and the corresponding multiplication and composition operators are investigated. The optimality of the obtained results is illustrated by a variety of examples, including those of discrete and continuous types. The book is primarily aimed at researchers in single or multivariable operator theory.
Book Synopsis Multivariable Operator Theory by : Ernst Albrecht
Download or read book Multivariable Operator Theory written by Ernst Albrecht and published by Springer Nature. This book was released on 2024-01-22 with total page 893 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Jörg Eschmeier made a number of fundamental contributions to the development of operator theory and related topics. The chapters in this volume, compiled in his memory, are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
Book Synopsis Issues in General and Specialized Mathematics Research: 2013 Edition by :
Download or read book Issues in General and Specialized Mathematics Research: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in General and Specialized Mathematics Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about General Mathematics. The editors have built Issues in General and Specialized Mathematics Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General Mathematics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Book Synopsis Zeta Functions for Two-Dimensional Shifts of Finite Type by : Jung-Chao Ban
Download or read book Zeta Functions for Two-Dimensional Shifts of Finite Type written by Jung-Chao Ban and published by American Mathematical Soc.. This book was released on 2013-01-25 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is concerned with zeta functions of two-dimensional shifts of finite type. A two-dimensional zeta function $\zeta^{0}(s)$, which generalizes the Artin-Mazur zeta function, was given by Lind for $\mathbb{Z}^{2}$-action $\phi$. In this paper, the $n$th-order zeta function $\zeta_{n}$ of $\phi$ on $\mathbb{Z}_{n\times \infty}$, $n\geq 1$, is studied first. The trace operator $\mathbf{T}_{n}$, which is the transition matrix for $x$-periodic patterns with period $n$ and height $2$, is rotationally symmetric. The rotational symmetry of $\mathbf{T}_{n}$ induces the reduced trace operator $\tau_{n}$ and $\zeta_{n}=\left(\det\left(I-s^{n}\tau_{n}\right)\right)^{-1}$. The zeta function $\zeta=\prod_{n=1}^{\infty} \left(\det\left(I-s^{n}\tau_{n}\right)\right)^{-1}$ in the $x$-direction is now a reciprocal of an infinite product of polynomials. The zeta function can be presented in the $y$-direction and in the coordinates of any unimodular transformation in $GL_{2}(\mathbb{Z})$. Therefore, there exists a family of zeta functions that are meromorphic extensions of the same analytic function $\zeta^{0}(s)$. The natural boundary of zeta functions is studied. The Taylor series for these zeta functions at the origin are equal with integer coefficients, yielding a family of identities, which are of interest in number theory. The method applies to thermodynamic zeta functions for the Ising model with finite range interactions.
Book Synopsis Notes on the Brown-Douglas-Fillmore Theorem by : Sameer Chavan
Download or read book Notes on the Brown-Douglas-Fillmore Theorem written by Sameer Chavan and published by Cambridge University Press. This book was released on 2021-10-07 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses the complete proof of the Brown-Douglas-Fillmore theorem along with a number of its applications.
Book Synopsis A Theory of Generalized Donaldson-Thomas Invariants by : Dominic D. Joyce
Download or read book A Theory of Generalized Donaldson-Thomas Invariants written by Dominic D. Joyce and published by American Mathematical Soc.. This book was released on 2011 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies generalized Donaldson-Thomas invariants $\bar{DT}{}^\alpha(\tau)$. They are rational numbers which `count' both $\tau$-stable and $\tau$-semistable coherent sheaves with Chern character $\alpha$ on $X$; strictly $\tau$-semistable sheaves must be counted with complicated rational weights. The $\bar{DT}{}^\alpha(\tau)$ are defined for all classes $\alpha$, and are equal to $DT^\alpha(\tau)$ when it is defined. They are unchanged under deformations of $X$, and transform by a wall-crossing formula under change of stability condition $\tau$. To prove all this, the authors study the local structure of the moduli stack $\mathfrak M$ of coherent sheaves on $X$. They show that an atlas for $\mathfrak M$ may be written locally as $\mathrm{Crit}(f)$ for $f:U\to{\mathbb C}$ holomorphic and $U$ smooth, and use this to deduce identities on the Behrend function $\nu_\mathfrak M$. They compute the invariants $\bar{DT}{}^\alpha(\tau)$ in examples, and make a conjecture about their integrality properties. They also extend the theory to abelian categories $\mathrm{mod}$-$\mathbb{C}Q\backslash I$ of representations of a quiver $Q$ with relations $I$ coming from a superpotential $W$ on $Q$.
Book Synopsis General Relativistic Self-Similar Waves that Induce an Anomalous Acceleration into the Standard Model of Cosmology by : Joel Smoller
Download or read book General Relativistic Self-Similar Waves that Induce an Anomalous Acceleration into the Standard Model of Cosmology written by Joel Smoller and published by American Mathematical Soc.. This book was released on 2012 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove that the Einstein equations for a spherically symmetric spacetime in Standard Schwarzschild Coordinates (SSC) close to form a system of three ordinary differential equations for a family of self-similar expansion waves, and the critical ($k=0$) Friedmann universe associated with the pure radiation phase of the Standard Model of Cosmology is embedded as a single point in this family. Removing a scaling law and imposing regularity at the center, they prove that the family reduces to an implicitly defined one-parameter family of distinct spacetimes determined by the value of a new acceleration parameter $a$, such that $a=1$ corresponds to the Standard Model. The authors prove that all of the self-similar spacetimes in the family are distinct from the non-critical $k\neq0$ Friedmann spacetimes, thereby characterizing the critical $k=0$ Friedmann universe as the unique spacetime lying at the intersection of these two one-parameter families. They then present a mathematically rigorous analysis of solutions near the singular point at the center, deriving the expansion of solutions up to fourth order in the fractional distance to the Hubble Length. Finally, they use these rigorous estimates to calculate the exact leading order quadratic and cubic corrections to the redshift vs luminosity relation for an observer at the center.
Book Synopsis The Lin-Ni's Problem for Mean Convex Domains by : Olivier Druet
Download or read book The Lin-Ni's Problem for Mean Convex Domains written by Olivier Druet and published by American Mathematical Soc.. This book was released on 2012 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove some refined asymptotic estimates for positive blow-up solutions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$, $\Omega$ being a smooth bounded domain of $\mathbb{R}^n$, $n\geq 3$. In particular, they show that concentration can occur only on boundary points with nonpositive mean curvature when $n=3$ or $n\geq 7$. As a direct consequence, they prove the validity of the Lin-Ni's conjecture in dimension $n=3$ and $n\geq 7$ for mean convex domains and with bounded energy. Recent examples by Wang-Wei-Yan show that the bound on the energy is a necessary condition.
Book Synopsis On First and Second Order Planar Elliptic Equations with Degeneracies by : Abdelhamid Meziani
Download or read book On First and Second Order Planar Elliptic Equations with Degeneracies written by Abdelhamid Meziani and published by American Mathematical Soc.. This book was released on 2012 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed. Properties of solutions, in a neighborhood of the degeneracy curve, are obtained through integral and series representations. An application to a second order elliptic equation with a punctual singularity is given.
Book Synopsis Second Order Analysis on $(\mathscr {P}_2(M),W_2)$ by : Nicola Gigli
Download or read book Second Order Analysis on $(\mathscr {P}_2(M),W_2)$ written by Nicola Gigli and published by American Mathematical Soc.. This book was released on 2012-02-22 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops a rigorous second order analysis on the space of probability measures on a Riemannian manifold endowed with the quadratic optimal transport distance $W_2$. The discussion includes: definition of covariant derivative, discussion of the problem of existence of parallel transport, calculus of the Riemannian curvature tensor, differentiability of the exponential map and existence of Jacobi fields. This approach does not require any smoothness assumption on the measures considered.
Book Synopsis Towards a Modulo $p$ Langlands Correspondence for GL$_2$ by : Christophe Breuil
Download or read book Towards a Modulo $p$ Langlands Correspondence for GL$_2$ written by Christophe Breuil and published by American Mathematical Soc.. This book was released on 2012-02-22 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors construct new families of smooth admissible $\overline{\mathbb{F}}_p$-representations of $\mathrm{GL}_2(F)$, where $F$ is a finite extension of $\mathbb{Q}_p$. When $F$ is unramified, these representations have the $\mathrm{GL}_2({\mathcal O}_F)$-socle predicted by the recent generalizations of Serre's modularity conjecture. The authors' motivation is a hypothetical mod $p$ Langlands correspondence.
Book Synopsis The Hermitian Two Matrix Model with an Even Quartic Potential by : Maurice Duits
Download or read book The Hermitian Two Matrix Model with an Even Quartic Potential written by Maurice Duits and published by American Mathematical Soc.. This book was released on 2012 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the two matrix model with an even quartic potential $W(y)=y^4/4+\alpha y^2/2$ and an even polynomial potential $V(x)$. The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices $M_1$. The vector equilibrium problem is defined for three measures, with external fields on the first and third measures and an upper constraint on the second measure. The proof is based on a steepest descent analysis of a $4\times4$ matrix valued Riemann-Hilbert problem that characterizes the correlation kernel for the eigenvalues of $M_1$. The authors' results generalize earlier results for the case $\alpha=0$, where the external field on the third measure was not present.
Book Synopsis Hopf Algebras and Congruence Subgroups by : Yorck Sommerhäuser
Download or read book Hopf Algebras and Congruence Subgroups written by Yorck Sommerhäuser and published by American Mathematical Soc.. This book was released on 2012 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove that the kernel of the action of the modular group on the center of a semisimple factorizable Hopf algebra is a congruence subgroup whenever this action is linear. If the action is only projective, we show that the projective kernel is a congruence subgroup. To do this, we introduce a class of generalized Frobenius-Schur indicators and endow it with an action of the modular group that is compatible with the original one.
