V. V. Karachik, “On an Expansion of Almansi Type”, Mat. Zametki, 83:3 (2008), 370–380; Math. Notes, 83:3 (2008), 335

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Matematicheskie Zametki, 2008, Volume 83, Issue 3, Pages 370–380
DOI: https://doi.org/10.4213/mzm4525 (Mi mzm4525)

This article is cited in 27 scientific papers (total in 27 papers)

On an Expansion of Almansi Type

V. V. Karachik

South Ural State University

Full-text PDF (446 kB) Citations (27)

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DOI: https://doi.org/10.4213/mzm4525

Abstract: We obtain an expansion of Almansi type for functions satisfying the equation

$\Delta_\lambda^mu=0$ , where

$\Delta_\lambda=\lambda_1\partial^2/\partial x_1^2+\dotsb+\lambda_n\partial^2/\partial x_n^2$ and

$\lambda_k\ne0$ .

Keywords: Almansi expansion, polyharmonic function, normalized system of functions, Laplace operator.

Received: 18.11.2006
Revised: 04.04.2007

English version:
Mathematical Notes, 2008, Volume 83, Issue 3, Pages 335–344
DOI: https://doi.org/10.1134/S000143460803005X

Bibliographic databases:

UDC: 517.956.22

Language: Russian

Citation: V. V. Karachik, “On an Expansion of Almansi Type”, Mat. Zametki, 83:3 (2008), 370–380; Math. Notes, 83:3 (2008), 335–344

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm4525

https://doi.org/10.4213/mzm4525

https://www.mathnet.ru/eng/mzm/v83/i3/p370

This publication is cited in the following 27 articles:

Karachik V., “Dirichlet and Neumann Boundary Value Problems For the Polyharmonic Equation in the Unit Ball”, Mathematics, 9:16 (2021), 1907
Karachik V., “Green'S Function of Dirichlet Problem For Biharmonic Equation in the Ball”, Complex Var. Elliptic Equ., 64:9 (2019), 1500–1521
Karachik V.V., Turmetov B.K., “On Green'S Function of the Robin Problem For the Poisson Equation”, Adv. Pure Appl. Math., 10:3 (2019), 203–213
V. V. Karachik, “The Green function of the Dirichlet problem for the biharmonic equation in a ball”, Comput. Math. Math. Phys., 59:1 (2019), 66–81
V. V. Karachik, “Riquier–Neumann problem for the polyharmonic equation in a ball”, Differ. Equ., 54:5 (2018), 648–657
V. V. Karachik, B. Kh. Turmetov, “On the Green's function for the third boundary value problem”, Siberian Adv. Math., 29:1 (2019), 32–43
V. V. Karachik, “Ob odnom predstavlenii funktsii Grina zadachi Dirikhle dlya bigarmonicheskogo uravneniya v share”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 10:4 (2018), 13–22
V. V. Karachik, B. T. Torebek, “On the Dirichlet–Riquier Problem for Biharmonic Equations”, Math. Notes, 102:1 (2017), 31–42
I. A. Gulyaschikh, “Razreshimost odnoi zadachi tipa Neimana dlya trigarmonicheskogo uravneniya v share”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 9:3 (2017), 5–12
V. V. Karachik, “Zadacha tipa Neimana dlya poligarmonicheskogo uravneniya v share”, Chelyab. fiz.-matem. zhurn., 2:4 (2017), 420–429
Yuan H., Karachik V.V., “Representations of super-holomorphic functions and their applications”, Complex Var. Elliptic Equ., 61:11 (2016), 1517–1532
E. Yu. Chistyakov, “O resheniyakh volnovogo uravneniya s mladshim chlenom”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 7:4 (2015), 74–76
V. V. Karachik, “Solution of the Dirichlet problem with polynomial data for the polyharmonic equation in a ball”, Diff Equat, 51:8 (2015), 1033
V. V. Karachik, “Funktsiya Grina zadachi Dirikhle dlya poligarmonicheskogo uravneniya v share pri polinomialnykh dannykh”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 14:4(2) (2014), 550–558
V. V. Karachik, “Construction of polynomial solutions to the Dirichlet problem for the polyharmonic equation in a ball”, Comput. Math. Math. Phys., 54:7 (2014), 1122–1143
Koshanov B.D., “On the Solvability of Boundary Value Problems For the Nonhomogeneous Polyharmonic Equation in a Ball”, International Conference on Analysis and Applied Mathematics, AIP Conference Proceedings, 1611, eds. Ashyralyev A., Malkowsky E., Amer Inst Physics, 2014, 119–126
Yuan H., Qiao Yu., “Solutions of the Dirac and Related Equations in Superspace”, Complex Var. Elliptic Equ., 59:9 (2014), 1315–1327
Karachik V.V., Antropova N.A., “Polynomial Solutions of the Dirichlet Problem for the Biharmonic Equation in the Ball”, Differ. Equ., 49:2 (2013), 251–256
Koshanov B.D., “Usloviya razreshimosti kraevykh zadach dlya neodnorodnogo poligarmonicheskogo uravneniya v share”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya: Matematika. Fizika, 31:11 (2013), 44–53
V. V. Karachik, “Application of the Almansi formula for constructing polynomial solutions to the Dirichlet problem for a second-order equation”, Russian Math. (Iz. VUZ), 56:6 (2012), 20–29

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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