Finding solution subspaces of the Laplace and heat equations isometric to spaces of real functions, and some of their applications

DOI10.1134/S0001434618050231zbMath1406.46018OpenAlexW2810243515WikidataQ129618880 ScholiaQ129618880MaRDI QIDQ1668090

D. N. Bushev, Yuriıı I. Kharkevich

Publication date: 31 August 2018

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434618050231

zbMATH Keywords

heat equationLaplace equationHölder's inequalityLebesgue pointAbel-Poisson delta kernelGauss-Weierstrass delta kernelspaces of convolutions

Mathematics Subject Classification ID

Heat equation (35K05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Banach spaces of continuous, differentiable or analytic functions (46E15)

Related Items (5)

Exact values of the approximations of differentiable functions by Poisson-type integrals ⋮ Asymptotic properties of the solutions of higher-order differential equations on generalized Hölder classes ⋮ Some applied aspects of the Dirac delta function ⋮ Some asymptotic properties of the solutions of Laplace equations in a unit disk ⋮ Isometry of the subspaces of solutions of systems of differential equations to the spaces of real functions

Cites Work

• Some properties of operators of Abel-Poisson type
• Approximation of conjugate functions by generalized Abel-Poisson operators
• Conditions of convergence almost everywhere for the convolution of a function with delta-shaped kernel to this function
• Approximation properties of Poisson integrals for the classes \(C_\beta^\psi H^\alpha\)
• Approximation of (ψ, β)-differentiable functions by Weierstrass integrals
• On new exact solutions of a nonlinear diffusion system that describes the growth of protein crystals
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