<電子ブック>
Spectral Theory of Differential Operators : Self-Adjoint Differential Operators / by V.A. Il'in
版 | 1st ed. 1995. |
---|---|
出版者 | (New York, NY : Springer US : Imprint: Springer) |
出版年 | 1995 |
大きさ | XII, 390 p : online resource |
著者標目 | *Il'in, V.A author SpringerLink (Online service) |
件 名 | LCSH:Differential equations FREE:Differential Equations |
一般注記 | 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 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 HTTP:URL=https://doi.org/10.1007/978-1-4615-1755-9 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
Springer eBooks | 9781461517559 |
|
電子リソース |
|
EB00202411 |
類似資料
この資料の利用統計
このページへのアクセス回数:7回
※2017年9月4日以降