Author
Béla Szőkefalvi-Nagy
Bio: Béla Szőkefalvi-Nagy is an academic researcher. The author has contributed to research in topics: Operator theory & Hilbert space. The author has an hindex of 11, co-authored 18 publications receiving 3499 citations.
Papers
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01 Jan 1970
TL;DR: In this article, the structure of operators of Class C 0.1 is discussed.Contractions and their Dilations, Geometrical and Spectral Properties of Dilations and Operator-Valued Analytic Functions are discussed.
Abstract: Contractions and Their Dilations.- Geometrical and Spectral Properties of Dilations.- Functional Calculus.- Extended Functional Calculus.- Operator-Valued Analytic Functions.- Functional Models.- Regular Factorizations and Invariant Subspaces.- Weak Contractions.- The Structure of C1.-Contractions.- The Structure of Operators of Class C0.
2,339 citations
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TL;DR: In this paper, the notion of a quantum dynamical semigroup is defined using the concept of a completely positive map and an explicit form of a bounded generator of such a semigroup onB(ℋ) is derived.
Abstract: The notion of a quantum dynamical semigroup is defined using the concept of a completely positive map. An explicit form of a bounded generator of such a semigroup onB(ℋ) is derived. This is a quantum analogue of the Levy-Khinchin formula. As a result the general form of a large class of Markovian quantum-mechanical master equations is obtained.
6,381 citations
TL;DR: In this paper, the authors discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order, and investigate the dependence of the solution on the order of the differential equation and on the initial condition.
3,047 citations
Book•
01 Aug 19941,655 citations
Book•
30 Sep 1997TL;DR: Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly real compact spaces Extensions and liftings of mappings Infinite dimensional manifolds Calculus on infinite dimensional manifold, infinite dimensional differential geometry Manifolds of Mappings Further applications References as mentioned in this paper.
Abstract: Introduction Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly realcompact spaces Extensions and liftings of mappings Infinite dimensional manifolds Calculus on infinite dimensional manifolds Infinite dimensional differential geometry Manifolds of mappings Further applications References Index.
1,291 citations
Book•
21 Dec 2009TL;DR: The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial) as mentioned in this paper.
Abstract: The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even the expert probabilist. This rigorous introduction to the basic theory is sufficiently self-contained to be accessible to graduate students in mathematics or related sciences, who have mastered probability theory at the graduate level, but have not necessarily been exposed to advanced notions of functional analysis, algebra or geometry. Useful background material is collected in the appendices and exercises are also included throughout to test the reader's understanding. Enumerative techniques, stochastic analysis, large deviations, concentration inequalities, disintegration and Lie algebras all are introduced in the text, which will enable readers to approach the research literature with confidence.
1,289 citations