Algebras Of Singular Integral Operators With Kernels Controlled By Multiple Norms

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Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms

Alexander Nagel,Fulvio Ricci,Elias M. Stein,Stephen Wainger
Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms Book PDF

Author : Alexander Nagel,Fulvio Ricci,Elias M. Stein,Stephen Wainger
Publisher : American Mathematical Soc.
Page : 141 pages
File Size : 46,7 Mb
Release : 2019-01-08
Category : Algebra
ISBN : 9781470434380

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Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms by Alexander Nagel,Fulvio Ricci,Elias M. Stein,Stephen Wainger Pdf

The authors study algebras of singular integral operators on R and nilpotent Lie groups that arise when considering the composition of Calderón-Zygmund operators with different homogeneities, such as operators occuring in sub-elliptic problems and those arising in elliptic problems. These algebras are characterized in a number of different but equivalent ways: in terms of kernel estimates and cancellation conditions, in terms of estimates of the symbol, and in terms of decompositions into dyadic sums of dilates of bump functions. The resulting operators are pseudo-local and bounded on for . . While the usual class of Calderón-Zygmund operators is invariant under a one-parameter family of dilations, the operators studied here fall outside this class, and reflect a multi-parameter structure.

Finite Fields, with Applications to Combinatorics

Kannan Soundararajan
Finite Fields with Applications to Combinatorics Book PDF

Author : Kannan Soundararajan
Publisher : American Mathematical Society
Page : 100 pages
File Size : 55,7 Mb
Release : 2022-11-09
Category : Mathematics
ISBN : 9781470469306

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Finite Fields, with Applications to Combinatorics by Kannan Soundararajan Pdf

This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn sequences and a magic trick of Persi Diaconis, and the polynomial time algorithm for primality testing due to Agrawal, Kayal and Saxena. The book forms the basis for a one term intensive course with students meeting weekly for multiple lectures and a discussion session. Readers can expect to develop familiarity with ideas in algebra (groups, rings and fields), and elementary number theory, which would help with later classes where these are developed in greater detail. And they will enjoy seeing the AKS primality test application tying together the many disparate topics from the book. The pre-requisites for reading this book are minimal: familiarity with proof writing, some linear algebra, and one variable calculus is assumed. This book is aimed at incoming undergraduate students with a strong interest in mathematics or computer science.

Crossed Products of Operator Algebras

Elias G. Katsoulis,Christopher Ramsey
Crossed Products of Operator Algebras Book PDF

Author : Elias G. Katsoulis,Christopher Ramsey
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 47,9 Mb
Release : 2019-04-10
Category : C*-algebras
ISBN : 9781470435455

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Crossed Products of Operator Algebras by Elias G. Katsoulis,Christopher Ramsey Pdf

The authors study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. They develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. They complement their generic results with the detailed study of many important special cases. In particular they study crossed products of tensor algebras, triangular AF algebras and various associated C -algebras. They make contributions to the study of C -envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. They also answer questions from the pertinent literature.

Maximal Functions, Littlewood–Paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting

Yongsheng Han,Ming-Yi Lee,Ji Li,Brett Wick
Maximal Functions Littlewood Paley Theory Riesz Transforms and Atomic Decomposition in the Multi Parameter Flag Setting Book PDF

Author : Yongsheng Han,Ming-Yi Lee,Ji Li,Brett Wick
Publisher : American Mathematical Society
Page : 118 pages
File Size : 45,8 Mb
Release : 2022-08-31
Category : Mathematics
ISBN : 9781470453459

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Maximal Functions, Littlewood–Paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting by Yongsheng Han,Ming-Yi Lee,Ji Li,Brett Wick Pdf

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Geodesics, Retracts, and the Norm-Preserving Extension Property in the Symmetrized Bidisc

Jim Agler,Zinaida Lykova,Nicholas Young
Geodesics Retracts and the Norm Preserving Extension Property in the Symmetrized Bidisc Book PDF

Author : Jim Agler,Zinaida Lykova,Nicholas Young
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 41,7 Mb
Release : 2019-04-10
Category : Functions of complex variables
ISBN : 9781470435493

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Geodesics, Retracts, and the Norm-Preserving Extension Property in the Symmetrized Bidisc by Jim Agler,Zinaida Lykova,Nicholas Young Pdf

A set V in a domain U in Cn has the norm-preserving extension property if every bounded holomorphic function on V has a holomorphic extension to U with the same supremum norm. We prove that an algebraic subset of the symmetrized bidisc

Differential Equations, Mathematical Modeling and Computational Algorithms

Vladimir Vasilyev
Differential Equations Mathematical Modeling and Computational Algorithms Book PDF

Author : Vladimir Vasilyev
Publisher : Springer Nature
Page : 294 pages
File Size : 54,9 Mb
Release : 2023-06-06
Category : Mathematics
ISBN : 9783031285059

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Differential Equations, Mathematical Modeling and Computational Algorithms by Vladimir Vasilyev Pdf

This book contains reports made at the International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, held in Belgorod, Russia, in October 2021 and is devoted to various aspects of the theory of differential equations and their applications in various branches of science. Theoretical papers devoted to the qualitative analysis of emerging mathematical objects, theorems of the existence and uniqueness of solutions to the boundary value problems under study are presented, and numerical algorithms for their solution are described. Some issues of mathematical modeling are also covered; in particular, in problems of economics, computational aspects of the theory of differential equations and boundary value problems are studied. The articles are written by well-known experts and are interesting and useful to a wide audience: mathematicians, representatives of applied sciences and students and postgraduates of universities engaged in applied mathematics.

Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

Yuesheng Xu,Qi Ye
Generalized Mercer Kernels and Reproducing Kernel Banach Spaces Book PDF

Author : Yuesheng Xu,Qi Ye
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 53,5 Mb
Release : 2019-04-10
Category : Banach spaces
ISBN : 9781470435509

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Generalized Mercer Kernels and Reproducing Kernel Banach Spaces by Yuesheng Xu,Qi Ye Pdf

This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer kernels to construct p-norm RKBSs for 1≤p≤∞ .

Maximal Subellipticity

Brian Street
Maximal Subellipticity Book PDF

Author : Brian Street
Publisher : Walter de Gruyter GmbH & Co KG
Page : 768 pages
File Size : 41,9 Mb
Release : 2023-07-03
Category : Mathematics
ISBN : 9783111085647

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Maximal Subellipticity by Brian Street Pdf

Maximally subelliptic partial differential equations (PDEs) are a far-reaching generalization of elliptic PDEs. Elliptic PDEs hold a special place: sharp results are known for general linear and even fully nonlinear elliptic PDEs. Over the past half-century, important results for elliptic PDEs have been generalized to maximally subelliptic PDEs. This text presents this theory and generalizes the sharp, interior regularity theory for general linear and fully nonlinear elliptic PDEs to the maximally subelliptic setting.

Time Changes of the Brownian Motion: Poincaré Inequality, Heat Kernel Estimate and Protodistance

Jun Kigami
Time Changes of the Brownian Motion Poincar Inequality Heat Kernel Estimate and Protodistance Book PDF

Author : Jun Kigami
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 47,9 Mb
Release : 2019-06-10
Category : Brownian motion processes
ISBN : 9781470436209

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Time Changes of the Brownian Motion: Poincaré Inequality, Heat Kernel Estimate and Protodistance by Jun Kigami Pdf

In this paper, time changes of the Brownian motions on generalized Sierpinski carpets including n-dimensional cube [0,1]n are studied. Intuitively time change corresponds to alteration to density of the medium where the heat flows. In case of the Brownian motion on [0,1]n, density of the medium is homogeneous and represented by the Lebesgue measure. The author's study includes densities which are singular to the homogeneous one. He establishes a rich class of measures called measures having weak exponential decay. This class contains measures which are singular to the homogeneous one such as Liouville measures on [0,1]2 and self-similar measures. The author shows the existence of time changed process and associated jointly continuous heat kernel for this class of measures. Furthermore, he obtains diagonal lower and upper estimates of the heat kernel as time tends to 0. In particular, to express the principal part of the lower diagonal heat kernel estimate, he introduces “protodistance” associated with the density as a substitute of ordinary metric. If the density has the volume doubling property with respect to the Euclidean metric, the protodistance is shown to produce metrics under which upper off-diagonal sub-Gaussian heat kernel estimate and lower near diagonal heat kernel estimate will be shown.

Spinors on Singular Spaces and the Topology of Causal Fermion Systems

Felix Finster,Niky Kamran
Spinors on Singular Spaces and the Topology of Causal Fermion Systems Book PDF

Author : Felix Finster,Niky Kamran
Publisher : American Mathematical Soc.
Page : 83 pages
File Size : 54,7 Mb
Release : 2019-06-10
Category : Electronic
ISBN : 9781470436216

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Spinors on Singular Spaces and the Topology of Causal Fermion Systems by Felix Finster,Niky Kamran Pdf

Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures are introduced and analyzed. The connection to the spin condition in differential topology is worked out. The constructions are illustrated by many simple examples such as the Euclidean plane, the two-dimensional Minkowski space, a conical singularity, a lattice system as well as the curvature singularity of the Schwarzschild space-time. As further examples, it is shown how complex and Kähler structures can be encoded in Riemannian fermion systems.

Moufang Sets and Structurable Division Algebras

Lien Boelaert,Tom De Medts,Anastasia Stavrova
Moufang Sets and Structurable Division Algebras Book PDF

Author : Lien Boelaert,Tom De Medts,Anastasia Stavrova
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 51,9 Mb
Release : 2019-06-10
Category : Combinatorial group theory
ISBN : 9781470435547

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Moufang Sets and Structurable Division Algebras by Lien Boelaert,Tom De Medts,Anastasia Stavrova Pdf

A Moufang set is essentially a doubly transitive permutation group such that each point stabilizer contains a normal subgroup which is regular on the remaining vertices; these regular normal subgroups are called the root groups, and they are assumed to be conjugate and to generate the whole group. It has been known for some time that every Jordan division algebra gives rise to a Moufang set with abelian root groups. The authors extend this result by showing that every structurable division algebra gives rise to a Moufang set, and conversely, they show that every Moufang set arising from a simple linear algebraic group of relative rank one over an arbitrary field k of characteristic different from 2 and 3 arises from a structurable division algebra. The authors also obtain explicit formulas for the root groups, the τ-map and the Hua maps of these Moufang sets. This is particularly useful for the Moufang sets arising from exceptional linear algebraic groups.

Extended States for the Schrödinger Operator with Quasi-Periodic Potential in Dimension Two

Yulia Karpeshina,Roman Shterenberg
Extended States for the Schr dinger Operator with Quasi Periodic Potential in Dimension Two Book PDF

Author : Yulia Karpeshina,Roman Shterenberg
Publisher : American Mathematical Soc.
Page : 139 pages
File Size : 41,8 Mb
Release : 2019-04-10
Category : Schrödinger equation
ISBN : 9781470435431

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Extended States for the Schrödinger Operator with Quasi-Periodic Potential in Dimension Two by Yulia Karpeshina,Roman Shterenberg Pdf

The authors consider a Schrödinger operator H=−Δ+V(x⃗ ) in dimension two with a quasi-periodic potential V(x⃗ ). They prove that the absolutely continuous spectrum of H contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves ei⟨ϰ⃗ ,x⃗ ⟩ in the high energy region. Second, the isoenergetic curves in the space of momenta ϰ⃗ corresponding to these eigenfunctions have the form of slightly distorted circles with holes (Cantor type structure). A new method of multiscale analysis in the momentum space is developed to prove these results. The result is based on a previous paper on the quasiperiodic polyharmonic operator (−Δ)l+V(x⃗ ), l>1. Here the authors address technical complications arising in the case l=1. However, this text is self-contained and can be read without familiarity with the previous paper.

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 : 51,5 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.

Automorphisms ofTwo-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane

William Goldman,Greg McShane,George Stantchev,Ser Peow Tan
Automorphisms ofTwo Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane Book PDF

Author : William Goldman,Greg McShane,George Stantchev,Ser Peow Tan
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 54,5 Mb
Release : 2019-06-10
Category : Automorphisms
ISBN : 9781470436148

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Automorphisms ofTwo-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane by William Goldman,Greg McShane,George Stantchev,Ser Peow Tan Pdf

The automorphisms of a two-generator free group F acting on the space of orientation-preserving isometric actions of F on hyperbolic 3-space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on that plane is an invariant subsystem, which reduces to an action of a group on by polynomial automorphisms preserving the cubic polynomial and an area form on the level surfaces .