On Fourier Series in Eigenfunctions of Elliptic Boundary Value Problems
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| 024 | 7 | 0 | |a 10.1515/GMJ.2003.401 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.1515/GMJ.2003.401 | ||
| 245 | 0 | 0 | |a On Fourier Series in Eigenfunctions of Elliptic Boundary Value Problems |h [Elektronische Daten] |c [M. S. Agranovich, B. A. Amosov] |
| 520 | 3 | |a We consider a general elliptic formally self-adjoint problem in a bounded domain with homogeneous boundary conditions under the assumption that the boundary and coefficients are infinitely smooth. The operator in 2(Ω) corresponding to this problem has an orthonormal basis { } of eigenfunctions, which are infinitely smooth in . However, the system { } is not a basis in Sobolev spaces (Ω) of high order. We note and discuss the following possibility: for an arbitrarily large , for each function ∈ (Ω) one can explicitly construct a function 0 ∈ (Ω) such that the Fourier series of the difference - 0 in the functions converges to this difference in (Ω). Moreover, the function ( ) is viewed as a solution of the corresponding nonhomogeneous elliptic problem and is not assumed to be known a priori; only the right-hand sides of the elliptic equation and the boundary conditions for are assumed to be given. These data are also sufficient for the computation of the Fourier coefficients of - 0. The function 0 is obtained by applying some linear operator to these right-hand sides. | |
| 540 | |a © Heldermann Verlag | ||
| 690 | 7 | |a Elliptic boundary value problems |2 nationallicence | |
| 690 | 7 | |a Fourier expansions in eigenfunctions |2 nationallicence | |
| 690 | 7 | |a Sobolev spaces |2 nationallicence | |
| 690 | 7 | |a unconditional convergence |2 nationallicence | |
| 700 | 1 | |a Agranovich |D M. S. |u Moscow Institute of Electronics and Mathematics, Moscow 109028, Russia. E-mail: msa.funcan@mtu-net.ru |4 aut | |
| 700 | 1 | |a Amosov |D B. A. |u Moscow Institute of Electronics and Mathematics, Moscow 109028, Russia. E-mail: amosov@orc.ru |4 aut | |
| 773 | 0 | |t Georgian Mathematical Journal |d Walter de Gruyter GmbH & Co. KG |g 10/3(2003-09), 401-410 |x 1072-947X |q 10:3<401 |1 2003 |2 10 |o GMJ | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/GMJ.2003.401 |q text/html |z Onlinezugriff via DOI |
| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1515/GMJ.2003.401 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Agranovich |D M. S. |u Moscow Institute of Electronics and Mathematics, Moscow 109028, Russia. E-mail: msa.funcan@mtu-net.ru |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Amosov |D B. A. |u Moscow Institute of Electronics and Mathematics, Moscow 109028, Russia. E-mail: amosov@orc.ru |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Georgian Mathematical Journal |d Walter de Gruyter GmbH & Co. KG |g 10/3(2003-09), 401-410 |x 1072-947X |q 10:3<401 |1 2003 |2 10 |o GMJ | ||
| 900 | 7 | |b CC0 |u http://creativecommons.org/publicdomain/zero/1.0 |2 nationallicence | |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-gruyter | ||