Matrix Functions Of Bounded Type An Interplay Between Function Theory And Operator Theory

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

Raúl E. Curto,In Sung Hwang,Woo Young Lee
Matrix Functions of Bounded Type An Interplay Between Function Theory and Operator Theory Book PDF

Author : Raúl E. Curto,In Sung Hwang,Woo Young Lee
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 42,5 Mb
Release : 2019-09-05
Category : Functions of bounded variation
ISBN : 9781470436247

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Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory by Raúl E. Curto,In Sung Hwang,Woo Young Lee Pdf

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.

Function Spaces, Theory and Applications

Ilia Binder,Damir Kinzebulatov,Javad Mashreghi
Function Spaces Theory and Applications Book PDF

Author : Ilia Binder,Damir Kinzebulatov,Javad Mashreghi
Publisher : Springer Nature
Page : 487 pages
File Size : 40,5 Mb
Release : 2024-01-12
Category : Mathematics
ISBN : 9783031392702

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Function Spaces, Theory and Applications by Ilia Binder,Damir Kinzebulatov,Javad Mashreghi Pdf

The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They also have several essential applications in other fields of mathematics and engineering, e.g., robust control engineering, signal and image processing, and theory of communication. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins, e.g. the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b), have also been the center of attention in the past two decades. Studying the Hilbert spaces of analytic functions and the operators acting on them, as well as their applications in other parts of mathematics or engineering were the main subjects of this program. During the program, the world leading experts on function spaces gathered and discussed the new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With more than 250 hours of lectures by prominent mathematicians, a wide variety of topics were covered. More explicitly, there were mini-courses and workshops on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Blaschke Products and Inner Functions, Discrete and Continuous Semigroups of Composition Operators, The Corona Problem, Non-commutative Function Theory, Drury-Arveson Space, and Convergence of Scattering Data and Non-linear Fourier Transform. At the end of each week, there was a high profile colloquium talk on the current topic. The program also contained two semester-long advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. The current volume features a more detailed version of some of the talks presented during the program.

The Mother Body Phase Transition in the Normal Matrix Model

Pavel M. Bleher,Guilherme L. F. Silva
The Mother Body Phase Transition in the Normal Matrix Model Book PDF

Author : Pavel M. Bleher,Guilherme L. F. Silva
Publisher : American Mathematical Soc.
Page : 144 pages
File Size : 51,8 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470441845

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The Mother Body Phase Transition in the Normal Matrix Model by Pavel M. Bleher,Guilherme L. F. Silva Pdf

In this present paper, the authors consider the normal matrix model with cubic plus linear potential.

Degree Theory of Immersed Hypersurfaces

Harold Rosenberg,Graham Smith
Degree Theory of Immersed Hypersurfaces Book PDF

Author : Harold Rosenberg,Graham Smith
Publisher : American Mathematical Soc.
Page : 62 pages
File Size : 51,5 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470441852

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Degree Theory of Immersed Hypersurfaces by Harold Rosenberg,Graham Smith Pdf

The authors develop a degree theory for compact immersed hypersurfaces of prescribed $K$-curvature immersed in a compact, orientable Riemannian manifold, where $K$ is any elliptic curvature function.

A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth

Jaroslav Nešetřil,Patrice Ossona de Mendez
A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree Depth Book PDF

Author : Jaroslav Nešetřil,Patrice Ossona de Mendez
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 45,9 Mb
Release : 2020-04-03
Category : Education
ISBN : 9781470440657

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A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth by Jaroslav Nešetřil,Patrice Ossona de Mendez Pdf

In this paper the authors introduce a general framework for the study of limits of relational structures and graphs in particular, which is based on a combination of model theory and (functional) analysis. The authors show how the various approaches to graph limits fit to this framework and that the authors naturally appear as “tractable cases” of a general theory. As an outcome of this, the authors provide extensions of known results. The authors believe that this puts these into a broader context. The second part of the paper is devoted to the study of sparse structures. First, the authors consider limits of structures with bounded diameter connected components and prove that in this case the convergence can be “almost” studied component-wise. They also propose the structure of limit objects for convergent sequences of sparse structures. Eventually, they consider the specific case of limits of colored rooted trees with bounded height and of graphs with bounded tree-depth, motivated by their role as “elementary bricks” these graphs play in decompositions of sparse graphs, and give an explicit construction of a limit object in this case. This limit object is a graph built on a standard probability space with the property that every first-order definable set of tuples is measurable. This is an example of the general concept of modeling the authors introduce here. Their example is also the first “intermediate class” with explicitly defined limit structures where the inverse problem has been solved.

The Bounded and Precise Word Problems for Presentations of Groups

S. V. Ivanov
The Bounded and Precise Word Problems for Presentations of Groups Book PDF

Author : S. V. Ivanov
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 55,8 Mb
Release : 2020-05-13
Category : Education
ISBN : 9781470441432

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The Bounded and Precise Word Problems for Presentations of Groups by S. V. Ivanov Pdf

The author introduces and studies the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in PSPACE, i.e., it can be solved in polynomial space. The main technical result of the paper states that, for certain finite presentations of groups, which include the Baumslag-Solitar one-relator groups and free products of cyclic groups, the bounded word problem and the precise word problem can be solved in polylogarithmic space. As consequences of developed techniques that can be described as calculus of brackets, the author obtains polylogarithmic space bounds for the computational complexity of the diagram problem for free groups, for the width problem for elements of free groups, and for computation of the area defined by polygonal singular closed curves in the plane. The author also obtains polynomial time bounds for these problems.

An Elementary Recursive Bound for Effective Positivstellensatz and Hilbert’s 17th Problem

Henri Lombardi,Daniel Perrucci,Marie-Françoise Roy
An Elementary Recursive Bound for Effective Positivstellensatz and Hilbert s 17th Problem Book PDF

Author : Henri Lombardi,Daniel Perrucci,Marie-Françoise Roy
Publisher : American Mathematical Soc.
Page : 113 pages
File Size : 51,9 Mb
Release : 2020-04-03
Category : Education
ISBN : 9781470441081

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An Elementary Recursive Bound for Effective Positivstellensatz and Hilbert’s 17th Problem by Henri Lombardi,Daniel Perrucci,Marie-Françoise Roy Pdf

The authors prove an elementary recursive bound on the degrees for Hilbert's 17th problem. More precisely they express a nonnegative polynomial as a sum of squares of rational functions and obtain as degree estimates for the numerators and denominators the following tower of five exponentials 222d4k where d is the number of variables of the input polynomial. The authors' method is based on the proof of an elementary recursive bound on the degrees for Stengle's Positivstellensatz. More precisely the authors give an algebraic certificate of the emptyness of the realization of a system of sign conditions and obtain as degree bounds for this certificate a tower of five exponentials, namely 22(2max{2,d}4k+s2kmax{2,d}16kbit(d)) where d is a bound on the degrees, s is the number of polynomials and k is the number of variables of the input polynomials.

Rigid Character Groups, Lubin-Tate Theory, and (φ,Γ)-Modules

Laurent Berger,Peter Schneider,Bingyong Xie
Rigid Character Groups Lubin Tate Theory and Modules Book PDF

Author : Laurent Berger,Peter Schneider,Bingyong Xie
Publisher : American Mathematical Soc.
Page : 75 pages
File Size : 42,8 Mb
Release : 2020-04-03
Category : Education
ISBN : 9781470440732

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Rigid Character Groups, Lubin-Tate Theory, and (φ,Γ)-Modules by Laurent Berger,Peter Schneider,Bingyong Xie Pdf

The construction of the p-adic local Langlands correspondence for GL2(Qp) uses in an essential way Fontaine's theory of cyclotomic (φ,Γ)-modules. Here cyclotomic means that Γ=Gal(Qp(μp∞)/Qp) is the Galois group of the cyclotomic extension of Qp. In order to generalize the p-adic local Langlands correspondence to GL2(L), where L is a finite extension of Qp, it seems necessary to have at our disposal a theory of Lubin-Tate (φ,Γ)-modules. Such a generalization has been carried out, to some extent, by working over the p-adic open unit disk, endowed with the action of the endomorphisms of a Lubin-Tate group. The main idea of this article is to carry out a Lubin-Tate generalization of the theory of cyclotomic (φ,Γ)-modules in a different fashion. Instead of the p-adic open unit disk, the authors work over a character variety that parameterizes the locally L-analytic characters on oL. They study (φ,Γ)-modules in this setting and relate some of them to what was known previously.

Affine Flag Varieties and Quantum Symmetric Pairs

Zhaobing Fan,Chun-Ju Lai,Yiqiang Li,Li Luo,Weiqiang Wang
Affine Flag Varieties and Quantum Symmetric Pairs Book PDF

Author : Zhaobing Fan,Chun-Ju Lai,Yiqiang Li,Li Luo,Weiqiang Wang
Publisher : American Mathematical Soc.
Page : 123 pages
File Size : 47,5 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470441753

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Affine Flag Varieties and Quantum Symmetric Pairs by Zhaobing Fan,Chun-Ju Lai,Yiqiang Li,Li Luo,Weiqiang Wang Pdf

The quantum groups of finite and affine type $A$ admit geometric realizations in terms of partial flag varieties of finite and affine type $A$. Recently, the quantum group associated to partial flag varieties of finite type $B/C$ is shown to be a coideal subalgebra of the quantum group of finite type $A$.

Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees

Rodney G. Downey,Keng Meng Ng,Reed Solomon
Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees Book PDF

Author : Rodney G. Downey,Keng Meng Ng,Reed Solomon
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 44,5 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470441623

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Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees by Rodney G. Downey,Keng Meng Ng,Reed Solomon Pdf

First, there are sets with minimal weak truth table degree which bound noncomputable computably enumerable sets under Turing reducibility. Second, no set with computable enumerable Turing degree can have minimal weak truth table degree. Third, no $Delta^0_2$ set which Turing bounds a promptly simple set can have minimal weak truth table degree.

Localization for $THH(ku)$ and the Topological Hochschild and Cyclic Homology of Waldhausen Categories

Andrew J. Blumberg,Michael A. Mandell
Localization for THH ku and the Topological Hochschild and Cyclic Homology of Waldhausen Categories Book PDF

Author : Andrew J. Blumberg,Michael A. Mandell
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 46,9 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470441784

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Localization for $THH(ku)$ and the Topological Hochschild and Cyclic Homology of Waldhausen Categories by Andrew J. Blumberg,Michael A. Mandell Pdf

The authors resolve the longstanding confusion about localization sequences in $THH$ and $TC$ and establish a specialized devissage theorem.

Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

Luigi Ambrosio,Andrea Mondino,Giuseppe Savaré
Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces Book PDF

Author : Luigi Ambrosio,Andrea Mondino,Giuseppe Savaré
Publisher : American Mathematical Soc.
Page : 121 pages
File Size : 40,5 Mb
Release : 2020-02-13
Category : Education
ISBN : 9781470439132

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Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces by Luigi Ambrosio,Andrea Mondino,Giuseppe Savaré Pdf

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.

Hodge Ideals

Mircea Mustaţă,Mihnea Popa
Hodge Ideals Book PDF

Author : Mircea Mustaţă,Mihnea Popa
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 55,6 Mb
Release : 2020-02-13
Category : Education
ISBN : 9781470437817

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Hodge Ideals by Mircea Mustaţă,Mihnea Popa Pdf

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)

Michael Handel,Lee Mosher
Subgroup Decomposition in Out Fn Book PDF

Author : Michael Handel,Lee Mosher
Publisher : American Mathematical Soc.
Page : 276 pages
File Size : 45,9 Mb
Release : 2020-05-13
Category : Education
ISBN : 9781470441135

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Subgroup Decomposition in Out(Fn) by Michael Handel,Lee Mosher Pdf

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.

The Triangle-Free Process and the Ramsey Number R(3,k)

Gonzalo Fiz Pontiveros,Simon Griffiths,Robert Morris
The Triangle Free Process and the Ramsey Number R 3 k Book PDF

Author : Gonzalo Fiz Pontiveros,Simon Griffiths,Robert Morris
Publisher : American Mathematical Soc.
Page : 125 pages
File Size : 49,6 Mb
Release : 2020-04-03
Category : Education
ISBN : 9781470440718

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The Triangle-Free Process and the Ramsey Number R(3,k) by Gonzalo Fiz Pontiveros,Simon Griffiths,Robert Morris Pdf

The areas of Ramsey theory and random graphs have been closely linked ever since Erdős's famous proof in 1947 that the “diagonal” Ramsey numbers R(k) grow exponentially in k. In the early 1990s, the triangle-free process was introduced as a model which might potentially provide good lower bounds for the “off-diagonal” Ramsey numbers R(3,k). In this model, edges of Kn are introduced one-by-one at random and added to the graph if they do not create a triangle; the resulting final (random) graph is denoted Gn,△. In 2009, Bohman succeeded in following this process for a positive fraction of its duration, and thus obtained a second proof of Kim's celebrated result that R(3,k)=Θ(k2/logk). In this paper the authors improve the results of both Bohman and Kim and follow the triangle-free process all the way to its asymptotic end.