-PDF Download- Matrix Functions Of Bounded Type An Interplay Between Function Theory And Operator Theory EBOOK

Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory

Author: Raúl E. Curto

Publisher: American Mathematical Soc.

Published: 2019-09-05

Total Pages: 100

ISBN-13: 1470436248

In this paper, the authors study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. They first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. They propose a new notion of tensored-scalar singularity, and then answer questions on Hankel operators with matrix-valued bounded type symbols. They also examine an interpolation problem related to a certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejér Interpolation Problem for matrix rational functions. The authors then extend the H∞-functional calculus to an H∞¯¯¯¯¯¯¯¯¯+H∞-functional calculus for the compressions of the shift. Next, the authors consider the subnormality of Toeplitz operators with matrix-valued bounded type symbols and, in particular, the matrix-valued version of Halmos's Problem 5 and then establish a matrix-valued version of Abrahamse's Theorem. They also solve a subnormal Toeplitz completion problem of 2×2 partial block Toeplitz matrices. Further, they establish a characterization of hyponormal Toeplitz pairs with matrix-valued bounded type symbols and then derive rank formulae for the self-commutators of hyponormal Toeplitz pairs.

Compact Quotients of Cahen-Wallach Spaces

Author: Ines Kath

Publisher: American Mathematical Soc.

Published: 2020-02-13

Total Pages: 84

ISBN-13: 1470441039

DOWNLOAD EBOOK →

Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous families of real parameters. The authors derive necessary and sufficient conditions for the existence of compact quotients of Cahen-Wallach spaces in terms of these parameters.

A Local Relative Trace Formula for the Ginzburg-Rallis Model: The Geometric Side

Author: Chen Wan

Publisher: American Mathematical Soc.

Published: 2019-12-02

Total Pages: 90

ISBN-13: 1470436868

DOWNLOAD EBOOK →

Following the method developed by Waldspurger and Beuzart-Plessis in their proofs of the local Gan-Gross-Prasad conjecture, the author is able to prove the geometric side of a local relative trace formula for the Ginzburg-Rallis model. Then by applying such formula, the author proves a multiplicity formula of the Ginzburg-Rallis model for the supercuspidal representations. Using that multiplicity formula, the author proves the multiplicity one theorem for the Ginzburg-Rallis model over Vogan packets in the supercuspidal case.

Time-Like Graphical Models

Author: Tvrtko Tadić

Publisher: American Mathematical Soc.

Published: 2019-12-02

Total Pages: 170

ISBN-13: 147043685X

DOWNLOAD EBOOK →

The author studies continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. In 2011, Burdzy and Pal proposed a continuous version of graphical models indexed by graphs with an embedded time structure— so-called time-like graphs. The author extends the notion of time-like graphs and finds properties of processes indexed by them. In particular, the author solves the conjecture of uniqueness of the distribution for the process indexed by graphs with infinite number of vertices. The author provides a new result showing the stochastic heat equation as a limit of the sequence of natural Brownian motions on time-like graphs. In addition, the author's treatment of time-like graphical models reveals connections to Markov random fields, martingales indexed by directed sets and branching Markov processes.

Quadratic Vector Equations on Complex Upper Half-Plane

Author: Oskari Ajanki

Publisher: American Mathematical Soc.

Published: 2019-12-02

Total Pages: 133

ISBN-13: 1470436833

DOWNLOAD EBOOK →

The authors consider the nonlinear equation −1m=z+Sm with a parameter z in the complex upper half plane H, where S is a positivity preserving symmetric linear operator acting on bounded functions. The solution with values in H is unique and its z-dependence is conveniently described as the Stieltjes transforms of a family of measures v on R. In a previous paper the authors qualitatively identified the possible singular behaviors of v: under suitable conditions on S we showed that in the density of v only algebraic singularities of degree two or three may occur. In this paper the authors give a comprehensive analysis of these singularities with uniform quantitative controls. They also find a universal shape describing the transition regime between the square root and cubic root singularities. Finally, motivated by random matrix applications in the authors' companion paper they present a complete stability analysis of the equation for any z∈H, including the vicinity of the singularities.

Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

Author: Luigi Ambrosio

Publisher: American Mathematical Soc.

Published: 2020-02-13

Total Pages: 121

ISBN-13: 1470439131

DOWNLOAD EBOOK →

The aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,d,m). On the geometric side, the authors' new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, the authors' new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong CD∗(K,N) condition of Bacher-Sturm.

Quasi-periodic Standing Wave Solutions of Gravity-Capillary Water Waves

Author: Massimiliano Berti

Publisher: American Mathematical Soc.

Published: 2020-04-03

Total Pages: 171

ISBN-13: 1470440695

DOWNLOAD EBOOK →

The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.

Cornered Heegaard Floer Homology

Author: Christopher L Douglas

Publisher: American Mathematical Soc.

Published: 2020-02-13

Total Pages: 111

ISBN-13: 1470437716

DOWNLOAD EBOOK →

Bordered Floer homology assigns invariants to 3-manifolds with boundary, such that the Heegaard Floer homology of a closed 3-manifold, split into two pieces, can be recovered as a tensor product of the bordered invariants of the pieces. The authors construct cornered Floer homology invariants of 3-manifolds with codimension-2 corners and prove that the bordered Floer homology of a 3-manifold with boundary, split into two pieces with corners, can be recovered as a tensor product of the cornered invariants of the pieces.

Hodge Ideals

Author: Mircea Mustaţă

Publisher: American Mathematical Soc.

Published: 2020-02-13

Total Pages: 78

ISBN-13: 1470437813

DOWNLOAD EBOOK →

The authors use methods from birational geometry to study the Hodge filtration on the localization along a hypersurface. This filtration leads to a sequence of ideal sheaves, called Hodge ideals, the first of which is a multiplier ideal. They analyze their local and global properties, and use them for applications related to the singularities and Hodge theory of hypersurfaces and their complements.

Subgroup Decomposition in Out(Fn)

Author: Michael Handel

Publisher: American Mathematical Soc.

Published: 2020-05-13

Total Pages: 276

ISBN-13: 1470441136

DOWNLOAD EBOOK →

In this work the authors develop a decomposition theory for subgroups of Out(Fn) which generalizes the decomposition theory for individual elements of Out(Fn) found in the work of Bestvina, Feighn, and Handel, and which is analogous to the decomposition theory for subgroups of mapping class groups found in the work of Ivanov.