UID:
almahu_9947363102702882
Umfang:
XII, 390 p.
,
online resource.
ISBN:
9781461517559
Inhalt:
In this fully-illustrated textbook, the author examines the spectral theory of self-adjoint elliptic operators. Chapters focus on the problems of convergence and summability of spectral decompositions about the fundamental functions of elliptic operators of the second order. The author's work offers a novel method for estimation of the remainder term of a spectral function and its Riesz means without recourse to the traditional Carleman technique and Tauberian theorem apparatus.
Anmerkung:
1. Expansion in the Fundamental System of Functions of the Laplace Operator -- 1.1 Fundamental Systems of Functions and Their Properties -- 1.2 Fractional Kernels -- 1.3 Estimate for the Remainder Term of a Spectral Function in the Metric L2 and the Resulting Corollaries -- 1.4 Exact Conditions for the Localization and Uniform Convergence of Expansions with Respect to an Arbitrary FSF in the Sobolev-Liouville Classes -- 1.5 On the Potential Generalization of the Theory -- Comments on Chapter 1 -- 2. Spectral Decompositions Corresponding to an Arbitrary Self-Adjoint Nonnegative Extension of the Laplace Operator -- 2.1 Self-Adjoint Nonnegative Extensions of Elliptic Operators. Ordered Spectral Representations of the Space L2. Classes of Differentiate Functions of N Variables -- 2.2 Formulation and Analysis of Main Results -- 2.3 Certain Properties of the Fundamental Functions of an Arbitrary Ordered Spectral Representation in the Space L2 -- 2.4 Proof of Negative Theorem 2.1 -- 2.5 Proof of Positive Theorem 2.3 -- 2.6 Estimate for the Remainder Term of the Riesz Means of a Spectral Function in the Metric L2 -- 2.7 Estimate for the Remainder Term of the Riesz Means of a Spectral Function in the Metric L2 -- Comments on Chapter 2 -- 3. On the Riesz Equisummability of Spectral Decompositions in the Classical and the Generalized Sense -- 3.1 On the Riesz Equisummability of Spectral Decompositions in the Classical Sense -- 3.2 On the Riesz Equisummability of Spectral Decompositions in the Generalized Sense -- Comments on Chapter 3 -- 4. Self-Adjoint Nonnegative Extensions of an Elliptic Operator of Second Order -- 4.1 Ancillary Propositions about Fundamental Functions -- 4.2 Theorems of Negative Type -- 4.3 Theorems of Positive Type -- Comments on Chapter 4 -- Appendix 1. Conditions for the Uniform Convergence of Multiple Trigonometric Fourier Series with Spherical Partial Sums -- Appendix 2. Conditions for the Uniform Convergence of Decompositions in Eigenfunctions of the First, Second, and Third Boundary-Value Problems for an Elliptic Operator of Second Order -- Epilogue -- References.
In:
Springer eBooks
Weitere Ausg.:
Printed edition: ISBN 9780306110375
Sprache:
Englisch
DOI:
10.1007/978-1-4615-1755-9
URL:
http://dx.doi.org/10.1007/978-1-4615-1755-9
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