Harmonic wavelets in boundary value problems for harmonic and biharmonic functions

We consider boundary value problems in a disk and in a ring for homogeneous equations with the Laplace operator of the first and second orders. Solutions are represented in terms of bases of harmonic wavelets in Hardy spaces of harmonic functions in a disk and in a ring, which were constructed earli...

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Published in:Proceedings of the Steklov Institute of Mathematics Vol. 273; no. Suppl 1; pp. 142 - 159
Main Authors: Subbotin, Yu. N., Chernykh, N. I.
Format: Journal Article
Language:English
Published: Dordrecht SP MAIK Nauka/Interperiodica 01.07.2011
Subjects:
Mathematics
Mathematics and Statistics
Laplace operator
disk
harmonic and biharmonic functions
harmonic wavelets
ring
boundary value problems
ISSN:0081-5438, 1531-8605
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Abstract We consider boundary value problems in a disk and in a ring for homogeneous equations with the Laplace operator of the first and second orders. Solutions are represented in terms of bases of harmonic wavelets in Hardy spaces of harmonic functions in a disk and in a ring, which were constructed earlier.
AbstractList We consider boundary value problems in a disk and in a ring for homogeneous equations with the Laplace operator of the first and second orders. Solutions are represented in terms of bases of harmonic wavelets in Hardy spaces of harmonic functions in a disk and in a ring, which were constructed earlier.
Author Chernykh, N. I.
Subbotin, Yu. N.
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Issue Suppl 1
Keywords Laplace operator
disk
harmonic and biharmonic functions
harmonic wavelets
ring
boundary value problems
Language English
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References SubbotinYu. N.ChernykhN. I.Izv. Ross. Akad. Nauk, Ser. Mat.20006411451752583
MeyerY.Ondelettes et Opérateurs1990Paris(Hermann
OffinD.OskolkovK.Constr. Approx.19639319121577510.1007/BF01198009
SubbotinYu. N.ChernykhN. I.Proc. Internat. Stechkin Summer School on Function Theory2007TulaIzd. Tul’sk. Gos. Univ.129149
Lavrent’evM. A.ShabatB. V.Methods of the Theory of Functions of a Complex Variable1965MoscowNauka
TikhonovA. N.SamarskiiA. A.Equations of Mathematical Physics1966MoscowNauka
A. Zygmund, Trigonometric Series (Cambridge Univ. Press, 1959; Mir, Moscow, 1965), Vol. 1 [in Russian].
A. N. Tikhonov (6359_CR6) 1966
Yu. N. Subbotin (6359_CR1) 2007
D. Offin (6359_CR3) 1963; 9
6359_CR7
Yu. N. Subbotin (6359_CR4) 2000; 64
Y. Meyer (6359_CR2) 1990
M. A. Lavrent’ev (6359_CR5) 1965
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– reference: A. Zygmund, Trigonometric Series (Cambridge Univ. Press, 1959; Mir, Moscow, 1965), Vol. 1 [in Russian].
– reference: TikhonovA. N.SamarskiiA. A.Equations of Mathematical Physics1966MoscowNauka
– reference: MeyerY.Ondelettes et Opérateurs1990Paris(Hermann
– reference: OffinD.OskolkovK.Constr. Approx.19639319121577510.1007/BF01198009
– reference: SubbotinYu. N.ChernykhN. I.Proc. Internat. Stechkin Summer School on Function Theory2007TulaIzd. Tul’sk. Gos. Univ.129149
– reference: Lavrent’evM. A.ShabatB. V.Methods of the Theory of Functions of a Complex Variable1965MoscowNauka
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  volume-title: Proc. Internat. Stechkin Summer School on Function Theory
  year: 2007
  ident: 6359_CR1
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  year: 1965
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  doi: 10.4213/im277
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  year: 1990
  ident: 6359_CR2
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  start-page: 319
  year: 1963
  ident: 6359_CR3
  publication-title: Constr. Approx.
  doi: 10.1007/BF01198009
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Title Harmonic wavelets in boundary value problems for harmonic and biharmonic functions
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