Flat Extensions Of Positive Moment Matrices Recursively Generated Relations
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Flat Extensions Of Positive Moment Matrices Recursively Generated Relations
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Author : Raúl E. Curto
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Flat Extensions Of Positive Moment Matrices Recursively Generated Relations written by Raúl E. Curto and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
In this book, the authors develop new computational tests for existence and uniqueness of representing measures $\mu$ in the Truncated Complex Moment Problem: $\gamma {ij}=\int \bar zizj\, d\mu$ $(0\le i+j\le 2n)$. Conditions for the existence of finitely atomic representing measures are expressed in terms of positivity and extension properties of the moment matrix $M(n)(\gamma )$ associated with $\gamma \equiv \gamma {(2n)}$: $\gamma {00}, \dots ,\gamma {0,2n},\dots ,\gamma {2n,0}$, $\gamma {00}>0$. This study includes new conditions for flat (i.e., rank-preserving) extensions $M(n+1)$ of $M(n)\ge 0$; each such extension corresponds to a distinct rank $M(n)$-atomic representing measure, and each such measure is minimal among representing measures in terms of the cardinality of its support. For a natural class of moment matrices satisfying the tests of recursive generation, recursive consistency, and normal consistency, the existence problem for minimal representing measures is reduced to the solubility of small systems of multivariable algebraic equations. In a variety of applications, including cases of the quartic moment problem ($n=2$), the text includes explicit contructions of minimal representing measures via the theory of flat extensions. Additional computational texts are used to prove non-existence of representing measures or the non-existence of minimal representing measures. These tests are used to illustrate, in very concrete terms, new phenomena, associated with higher-dimensional moment problems that do not appear in the classical one-dimensional moment problem.
Flat Extensions Of Positive Moment Matrices
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Author : Raúl E. Curto
language : en
Publisher: American Mathematical Society(RI)
Release Date : 1998
Flat Extensions Of Positive Moment Matrices written by Raúl E. Curto and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Functions of complex variables categories.
Develops computational tests for existence and uniqueness of representing measures $\mu$ in the Truncated Complex Moment Problem: $\gamma_{ij}=\int \bar z DEGREESiz DEGREESj\, d\mu$ $(0\1e i+j\1e 2n)$. This book expresses conditions for the existence of finitely atomic representing measures in terms
The Defect Relation Of Meromorphic Maps On Parabolic Manifolds
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Author : George Lawrence Ashline
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
The Defect Relation Of Meromorphic Maps On Parabolic Manifolds written by George Lawrence Ashline and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This book is intended for graduate students and research mathematicians working in several complex variables and analytic spaces.
Number Theory And Combinatorics
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Author : Bruce M. Landman
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-04-19
Number Theory And Combinatorics written by Bruce M. Landman and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-19 with Mathematics categories.
Over a career that spanned 60 years, Ronald L. Graham (known to all as Ron) made significant contributions to the fields of discrete mathematics, number theory, Ramsey theory, computational geometry, juggling and magical mathematics, and many more. Ron also was a mentor to generations of mathematicians, he gave countless talks and helped bring mathematics to a wider audience, and he held signifi cant leadership roles in the mathematical community. This volume is dedicated to the life and memory of Ron Graham, and includes 20-articles by leading scientists across a broad range of subjects that refl ect some of the many areas in which Ron worked.
Complexes Associated To Two Vectors And A Rectangular Matrix
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Author : Andrew R. Kustin
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Complexes Associated To Two Vectors And A Rectangular Matrix written by Andrew R. Kustin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book is intended for graduate student and research mathematicians interested in commutative rings and algebras.
Optimization Of Polynomials In Non Commuting Variables
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Author : Sabine Burgdorf
language : en
Publisher: Springer
Release Date : 2016-06-07
Optimization Of Polynomials In Non Commuting Variables written by Sabine Burgdorf and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-07 with Mathematics categories.
This book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.
Algebraic And Strong Splittings Of Extensions Of Banach Algebras
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Author : William G. Bade
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Algebraic And Strong Splittings Of Extensions Of Banach Algebras written by William G. Bade and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
In this volume, the authors address the following: Let $A$ be a Banach algebra, and let $\sum\:\ 0\rightarrow I\rightarrow\frak A\overset\pi\to\longrightarrow A\rightarrow 0$ be an extension of $A$, where $\frak A$ is a Banach algebra and $I$ is a closed ideal in $\frak A$. The extension splits algebraically (respectively, splits strongly) if there is a homomorphism (respectively, continuous homomorphism) $\theta\: A\rightarrow\frak A$ such that $\pi\circ\theta$ is the identity on $A$. Consider first for which Banach algebras $A$ it is true that every extension of $A$ in a particular class of extensions splits, either algebraically or strongly, and second for which Banach algebras it is true that every extension of $A$ in a particular class which splits algebraically also splits strongly. These questions are closely related to the question when the algebra $\frak A$ has a (strong) Wedderburn decomposition. The main technique for resolving these questions involves the Banach cohomology group $\cal H2(A,E)$ for a Banach $A$-bimodule $E$, and related cohomology groups. Later chapters are particularly concerned with the case where the ideal $I$ is finite-dimensional. Results are obtained for many of the standard Banach algebras $A$.
Matrix Completions Moments And Sums Of Hermitian Squares
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Author : Mihály Bakonyi
language : en
Publisher: Princeton University Press
Release Date : 2011-07-18
Matrix Completions Moments And Sums Of Hermitian Squares written by Mihály Bakonyi and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-18 with Mathematics categories.
Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than 200 exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to 600 references from books and journals from a wide variety of disciplines.
Realization Of Vector Fields And Dynamics Of Spatially Homogeneous Parabolic Equations
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Author : Edward Norman Dancer
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Realization Of Vector Fields And Dynamics Of Spatially Homogeneous Parabolic Equations written by Edward Norman Dancer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This book is intended for graduate students and research mathematicians working in partial differential equations.
Renormalized Self Intersection Local Times And Wick Power Chaos Processes
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Author : Michael B. Marcus
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Renormalized Self Intersection Local Times And Wick Power Chaos Processes written by Michael B. Marcus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Sufficient conditions are obtained for the continuity of renormalized self-intersection local times for the multiple intersections of a large class of strongly symmetric L vy processes in $R DEGREESm$, $m=1,2$. In $R DEGREES2$ these include Brownian motion and stable processes of index greater than 3/2, as well as many processes in their domains of attraction. In $R DEGREES1$ these include stable processes of index $3/4