The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators write by Volodymyr Koshmanenko. This book was released on 2016-07-08. The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators available in PDF, EPUB and Kindle. This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadratic forms, and the theory of rigged Hilbert spaces. The book will appeal to researchers in mathematics and mathematical physics studying the scales of densely embedded Hilbert spaces, the singular perturbations phenomenon, and singular interaction problems.
Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology
Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology write by Raul E Curto. This book was released on 2020-12-12. Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology available in PDF, EPUB and Kindle. This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas’ students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.
Jacobi Matrices and the Moment Problem
Jacobi Matrices and the Moment Problem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Jacobi Matrices and the Moment Problem write by Yurij M. Berezansky. This book was released on 2024-01-06. Jacobi Matrices and the Moment Problem available in PDF, EPUB and Kindle. This monograph presents the solution of the classical moment problem, the construction of Jacobi matrices and corresponding polynomials. The cases of strongly,trigonometric, complex and real two-dimensional moment problems are discussed, and the Jacobi-type matrices corresponding to the trigonometric moment problem are shown. The Berezansky theory of the expansion in generalized eigenvectors for corresponding set of commuting operators plays the key role in the proof of results. The book is recommended for researchers in fields of functional analysis, operator theory, mathematical physics, and engineers who deal with problems of coupled pendulums.
Singular Quadratic Forms in Perturbation Theory
Singular Quadratic Forms in Perturbation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Singular Quadratic Forms in Perturbation Theory write by Volodymyr Koshmanenko. This book was released on 2012-12-06. Singular Quadratic Forms in Perturbation Theory available in PDF, EPUB and Kindle. The notion of singular quadratic form appears in mathematical physics as a tool for the investigation of formal expressions corresponding to perturbations devoid of operator sense. Numerous physical models are based on the use of Hamiltonians containing perturba tion terms with singular properties. Typical examples of such expressions are Schrodin ger operators with O-potentials (-~ + AD) and Hamiltonians in quantum field theory with perturbations given in terms of operators of creation and annihilation (P(
Russian Journal of Mathematical Physics
Russian Journal of Mathematical Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Russian Journal of Mathematical Physics write by . This book was released on 2007. Russian Journal of Mathematical Physics available in PDF, EPUB and Kindle.
