Uniform convergence and Riesz summability of spectral resolutions

Sozanov, V. G.

doi:10.1007/bf01163280

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Uniform Convergence On Closed Domains1

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2018

2023

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Cited by 2 publications

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“…ByH α pq (Ω) denote the closure of C ∞ 0 (Ω) with respect to the norm of the space H α pq (Ω) . Using the methods of [1]- [2] for functions in the spaces with the mixed norm appropriate theorems on convergence of the spectral expansions associated with the Laplace operator on compact subsets of the domain were obtained in [36].…”

Section: Uniform Convergence On Closed Domainsmentioning

confidence: 99%

Localization of the Spectral Expansions Associated with the Partial Differential Operators

Rakhimov

2018

Nonlinear Systems and Complexity

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In this paper we discuss precise conditions of the summability and localization of the spectral expansions associated with various partial differential operators. In this we study the problems in the spaces of both smooth functions and singular distributions. We study spectral expansions of the distributions with the compact support and classify the distributions with the Sobolev spaces. All theorems are formulated in terms of the smoothness and degree of the regularizations.

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Section: Uniform Convergence On Closed Domainsmentioning

confidence: 99%