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Functions, Spaces, and Expansions

2010-05-27 Mathematics
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Release : 2010-05-27
Genre : Mathematics
Kind : eBook
Book Rating : 808/5 ( reviews)

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Book Synopsis Functions, Spaces, and Expansions by : Ole Christensen

Download or read book Functions, Spaces, and Expansions written by Ole Christensen. This book was released on 2010-05-27. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outside the field of pure mathematics. Although the treatment of each topic is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are fundamental to exploring the computational aspects of physics and engineering. Readers are expected to have a solid understanding of linear algebra, in Rn and in general vector spaces. Familiarity with the basic concepts of calculus and real analysis, including Riemann integrals and infinite series of real or complex numbers, is also required.

Set Function Spaces and Orthogonal Expansions of Finitely Additive Set Functions

1952
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Release : 1952
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Set Function Spaces and Orthogonal Expansions of Finitely Additive Set Functions by : Solomon Leader

Download or read book Set Function Spaces and Orthogonal Expansions of Finitely Additive Set Functions written by Solomon Leader. This book was released on 1952. Available in PDF, EPUB and Kindle. Book excerpt:

Expansions in Eigenfunctions of Selfadjoint Operators

1968 Boundary value problems
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Release : 1968
Genre : Boundary value problems
Kind : eBook
Book Rating : 496/5 ( reviews)

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Book Synopsis Expansions in Eigenfunctions of Selfadjoint Operators by : I͡Uriĭ Makarovich Berezanskiĭ

Download or read book Expansions in Eigenfunctions of Selfadjoint Operators written by I͡Uriĭ Makarovich Berezanskiĭ. This book was released on 1968. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Analysis and Applications

2018-04-11 Mathematics
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Release : 2018-04-11
Genre : Mathematics
Kind : eBook
Book Rating : 334/5 ( reviews)

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Book Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky

Download or read book Mathematical Analysis and Applications written by Michael Ruzhansky. This book was released on 2018-04-11. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Eigenfunction Expansions, Operator Algebras and Riemannian Symmetric Spaces

1996-09-25 Mathematics
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Release : 1996-09-25
Genre : Mathematics
Kind : eBook
Book Rating : 345/5 ( reviews)

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Book Synopsis Eigenfunction Expansions, Operator Algebras and Riemannian Symmetric Spaces by : Robert M Kauffman

Download or read book Eigenfunction Expansions, Operator Algebras and Riemannian Symmetric Spaces written by Robert M Kauffman. This book was released on 1996-09-25. Available in PDF, EPUB and Kindle. Book excerpt: This Research Note pays particular attention to studying the convergence of the expansion and to the case where D is a family of partial differential operators. All operators in the natural von Neumann algebraassociated with D, and also unbounded operators affiliated with this algebra, are expanded simultaneously in terms of generalized eigenprojections. These are operators which carry a natural space associated with D into its dual. The elements of the range of these eigenprojections are the eigenfunctions, which solve the appropriate eigenvalue equations by duality. The spectral measure is abstractly defined, but its absolute continuity with respect to Hausdorf measure on the joint spectrum is shown to occur when the eigenfunctions are very well-behaved. Uniqueness results are given showing that any two expansions arise from each other by a simple change of variable. A considerable effort has been made to keep the book self-contained for readers with a background in functional analysis including a basic understanding of the theory of von Neumann algebras. More advanced topics in functional analysis, andan introduction to differential geometry and differential operator theory, mostly without proofs, are given in an extensive section on background material.

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