On a Generalization of Bessel’s Inequality and the Riesz-Fischer Theorem to the Case of Expansions of Functions in L_p with p ≠ 2 in Eigenfunctions of the Laplace Operator on an Arbitrary N-Dimensional Domain

V. A. Il’in

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On a Generalization of Bessel’s Inequality and the Riesz-Fischer Theorem to the Case of Expansions of Functions in L_p with p ≠ 2 in Eigenfunctions of the Laplace Operator on an Arbitrary N-Dimensional Domain

机译：关于Bessel不等式的推广和Riesz-Fischer定理，在任意N维域上Laplace算子的本征函数中p_≠2的L_p中的函数展开

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This paper generalizes results obtained in [1] for expansions in a uniformly bounded orthonormal system to the case of expansions in eigenfunctions of the Laplace operator in an N-dimensional domain G, provided that the bilinear series sum from ∞ to k=1 of (u_k(x)u_k(y)/λ~n_k) (1) for the eigenvalues λ_k and the eigenfunctions u_k(x) with arbitrarily large n converges uniformly with respect to the pairs of points (x, y), one of which belongs to the entire closed domain G and the other, to an arbitrary strictly interior subdomain G.

机译：本文将在[1]中以均匀有界正交系统的展开的结果推广到N维域G中Laplace算子的本征函数展开的情况，条件是从∞到k = 1的双线性级数总和为（ u_k（x）u_k（y）/λ〜n_k）（1）对于特征值λ_k和具有任意大n的特征函数u_k（x）相对于点对（x，y）一致收敛到整个封闭域G，另一个到严格的内部子域G。

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《Doklady. Mathematics》 |2014年第1期|共5页
作者
V. A. Il’in;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Generalization; Bessel’s; Inequality;

机译：泛化;贝塞尔不等式;

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1. On a Generalization of Bessel’s Inequality and the Riesz-Fischer Theorem to the Case of Expansions of Functions in L_p with p ≠ 2 in Eigenfunctions of the Laplace Operator on an Arbitrary N-Dimensional Domain [J] . V. A. Il’in Doklady. Mathematics . 2014,第1期

机译：关于Bessel不等式的推广和Riesz-Fischer定理，在任意N维域上Laplace算子的本征函数中p_≠2的L_p中的函数展开
2. On the localization of eigenfunctions of the Laplace operator in rectangular domains [J] . Delitsyn A. L. Moscow University Physics Bulletin . 2016,第4期

机译：关于Laplace算符本征函数在矩形域中的定位
3. Some generalizations of Bessel and Flett potentials associated to the Laplace-Bessel differential operator [J] . Aliev Ilham A., Yucel Sinem Integral transforms and special functions . 2018,第1a4期

机译：与Laplace-Bessel差分操作员相关的贝塞尔和FLETT电位的一些概括
4. Conditions for uniformly convergence of expansions of continuous functions from Nikolskii classes in eigenfunction expansions of the Schr?dinger operator on closed domain [C] . Nur Amalina Binti Jamaludin, Anvarjon Ahmedov International Conference on Analysis and Applied Mathematics . 2014

机译：在闭合域的特征函数扩展中均匀函数均匀函数扩展的条件
5. Geometry of nodal sets and domains for eigenfunctions of Schroedinger operators. [D] . Haldane, Evan. 2008

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6. THE EIGENFUNCTION EXPANSION THEOREM FOR THE GENERAL SELF-ADJOINT SINGULAR ELLIPTIC PARTIAL DIFFERENTIAL OPERATOR. I. THE ANALYTICAL FOUNDATION [O] . Felix E. Browder 1954

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7. A Generalization of Neumann's Expansion of an Arbitrary Function in a Series of Bessel's Functions [O] . F. H. Jackson 1904

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8. Fatou Theorems and Maximal Functions for Eigenfunctions of the Laplace-Beltrami Operator in a Bidisk [R] . Sjoergen, P. 1982

机译：Bidisk中Laplace-Beltrami算子特征函数的Fatou定理和极大函数

On a Generalization of Bessel’s Inequality and the Riesz-Fischer Theorem to the Case of Expansions of Functions in L_p with p ≠ 2 in Eigenfunctions of the Laplace Operator on an Arbitrary N-Dimensional Domain

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