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Mat. Zametki, 2008, Volume 83, Issue 3, Pages 370–380 (Mi mz4525)  

This article is cited in 24 scientific papers (total in 24 papers)

On an Expansion of Almansi Type

V. V. Karachik

South Ural State University

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

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

Full text: PDF file (446 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2008, 83:3, 335–344

Bibliographic databases:

UDC: 517.956.22
Received: 18.11.2006
Revised: 04.04.2007

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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\paper On an Expansion of Almansi Type
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\pages 370--380
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\pages 335--344
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Karachik V.V., Antropova N.A., “On the solution of the inhomogeneous polyharmonic equation and the inhomogeneous Helmholtz equation”, Differ. Equ., 46:3 (2010), 387–399  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. V. V. Karachik, “Razlozheniya Almansi dlya nevyrozhdennykh operatorov vtorogo poryadka”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 2010, no. 3, 4–12  mathnet
    3. V. V. Karachik, “Construction of polynomial solutions to some boundary value problems for Poisson’s equation”, Comput. Math. Math. Phys., 51:9 (2011), 1567–1587  mathnet  crossref  mathscinet  isi
    4. V. V. Karachik, N. A. Antropova, “Postroenie polinomialnykh reshenii zadachi Dirikhle dlya bigarmonicheskogo uravneniya v share”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 2011, no. 5, 39–50  mathnet  elib
    5. 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  mathnet  crossref  mathscinet
    6. V. V. Karachik, N. A. Antropova, “O polinomialnykh resheniyakh zadachi Dirikhle dlya bigarmonicheskogo uravneniya v share”, Sib. zhurn. industr. matem., 15:2 (2012), 86–98  mathnet  mathscinet
    7. Valerii V. Karachik, “Polinomialnye resheniya zadachi Dirikhle dlya $3$-garmonicheskogo uravneniya v share”, Zhurn. SFU. Ser. Matem. i fiz., 5:4 (2012), 527–546  mathnet
    8. Qiao Yu., Yuan H., Yang H., “Normalized system for the super Laplace operator”, Adv. Appl. Clifford Algebr., 22:4 (2012), 1109–1128  crossref  mathscinet  zmath  isi  scopus
    9. 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  crossref  mathscinet  zmath  isi  elib  elib  scopus
    10. 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  elib
    11. 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  mathnet  crossref  elib
    12. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. 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  crossref  adsnasa  isi  scopus
    14. Yuan H., Qiao Yu., “Solutions of the Dirac and Related Equations in Superspace”, Complex Var. Elliptic Equ., 59:9 (2014), 1315–1327  crossref  mathscinet  zmath  isi  scopus
    15. E. Yu. Chistyakov, “O resheniyakh volnovogo uravneniya s mladshim chlenom”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 7:4 (2015), 74–76  mathnet  crossref  elib
    16. Yuan H., Karachik V.V., “Representations of super-holomorphic functions and their applications”, Complex Var. Elliptic Equ., 61:11 (2016), 1517–1532  crossref  mathscinet  zmath  isi  elib  scopus
    17. V. V. Karachik, B. T. Torebek, “On the Dirichlet–Riquier Problem for Biharmonic Equations”, Math. Notes, 102:1 (2017), 31–42  mathnet  crossref  crossref  mathscinet  isi  elib
    18. 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  mathnet  crossref  elib
    19. V. V. Karachik, “Zadacha tipa Neimana dlya poligarmonicheskogo uravneniya v share”, Chelyab. fiz.-matem. zhurn., 2:4 (2017), 420–429  mathnet  mathscinet  elib
    20. V. V. Karachik, “Riquier–Neumann problem for the polyharmonic equation in a ball”, Differ. Equ., 54:5 (2018), 648–657  crossref  crossref  mathscinet  isi  elib  elib  scopus
    21. 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  mathnet  crossref  crossref  elib
    22. 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  mathnet  crossref  elib
    23. Karachik V., “Green'S Function of Dirichlet Problem For Biharmonic Equation in the Ball”, Complex Var. Elliptic Equ., 64:9 (2019), 1500–1521  crossref  isi
    24. 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  crossref  isi
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