Geodesic
Dependence of the Convergence Domain of Spectral Expansions on the Geometry of the Set of Discontinuity of the Function Being Expanded
Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 178-193.

Voir la notice de l'article provenant de la source Math-Net.Ru

For piecewise smooth functions, we indicate their domains of convergence and Riecz summarizability of their spectral expansions related to the Laplace operator in $\mathbb R^n$, depending on the geometry of points of discontinuity of the function being expanded. 
@article{MZM_2006_79_2_a2,
     author = {Sh. A. Alimov},
     title = {Dependence of the {Convergence} {Domain} of {Spectral} {Expansions} on the {Geometry} of the {Set} of {Discontinuity} of the {Function} {Being} {Expanded}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {178--193},
     publisher = {mathdoc},
     volume = {79},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a2/}
}
TY  - JOUR
AU  - Sh. A. Alimov
TI  - Dependence of the Convergence Domain of Spectral Expansions on the Geometry of the Set of Discontinuity of the Function Being Expanded
JO  - Matematičeskie zametki
PY  - 2006
SP  - 178
EP  - 193
VL  - 79
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a2/
LA  - ru
ID  - MZM_2006_79_2_a2
ER  - 
%0 Journal Article
%A Sh. A. Alimov
%T Dependence of the Convergence Domain of Spectral Expansions on the Geometry of the Set of Discontinuity of the Function Being Expanded
%J Matematičeskie zametki
%D 2006
%P 178-193
%V 79
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a2/
%G ru
%F MZM_2006_79_2_a2
Sh. A. Alimov. Dependence of the Convergence Domain of Spectral Expansions on the Geometry of the Set of Discontinuity of the Function Being Expanded. Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 178-193. http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a2/

[1] Alimov Sh. A., Ilin V. A., Nikishin E. M., “Voprosy skhodimosti kratnykh trigonometricheskikh ryadov i spektralnykh razlozhenii. I; II”, UMN, 31:6 (1976), 28–83 ; 32:1 (1977), 107–130 | MR | Zbl | MR | Zbl

[2] Ilin V. A., “Teorema o razlozhimosti kusochno-gladkoi funktsii v ryad po sobstvennym funktsiyam proizvolnoi dvumernoi oblasti”, Dokl. AN SSSR, 109 (1956), 442–445 | MR

[3] Pinsky M. A., “Fourier inversion for piecewise smooth functions in several variables”, Proc. Amer. Math. Soc., 118 (1993), 903–910 | DOI | MR | Zbl

[4] Pinsky M., Taylor M., “Pointwise Fourier inversion: a wave equation approach”, J. Fourier Anal. Appl., 3 (1997), 647–703 | DOI | MR | Zbl

[5] Popov D. A., “Sfericheskaya skhodimost ryada i integrala Fure indikatora dvumernoi oblasti”, Tr. MIAN, 218, Nauka, M., 1997, 354–373 | MR | Zbl

[6] Brandolini L., Colzani L., “Localization and convergence of eigenfunction expansions”, J. Fourier Anal. Appl., 5:5 (1999), 431–447 | DOI | MR | Zbl

[7] Taylor M., “Pointwise Fourier inversion on tori and other compact manifolds”, J. Fourier Anal. Appl., 5:5 (1999), 449–463 | DOI | MR | Zbl

[8] Taylor M., “Eigenfunction expansions and the Pinsky phenomenon on compact manifolds”, J. Fourier Anal. Appl., 7:5 (2001), 507–522 | DOI | MR | Zbl

[9] Alimov Sh. A., “On the eigenfunction expansion of a piecewise smooth function”, J. Fourier Anal. Appl., 9:1 (2003), 67–76 | DOI | MR | Zbl

[10] Maslov V. P., “Svoistva absolyutnoi skhodimosti mnogomernykh ryadov Fure s tochki zreniya geometrii slabykh razryvov razlagaemykh funktsii”, Dokl. AN SSSR, 191:2 (1970), 275–278 | Zbl

[11] Maslov V. P., “O razlozhenii funktsii, zavisyaschei ot parametra, v absolyutno skhodyaschiisya ryad Fure po sobstvennym funktsiyam psevdodifferentsialnogo operatora”, UMN, 25:1 (151) (1970), 195–196 | MR | Zbl

[12] Fedoryuk M. V., Asimptotika: integraly i ryady, Nauka, M., 1987 | MR

[13] Arnold V. I., “Normalnye formy funktsii vblizi vyrozhdennykh kriticheskikh tochek, gruppy Veilya $A_k,D_k,E_k$ i lagranzhevy osobennosti”, Funktsion. analiz i ego prilozh., 6:4 (1972), 3–25 | MR

[14] Sobolev S. L., Uravneniya matematicheskoi fiziki, Nauka, M., 1966 | MR

[15] Hörmander L., On the Riesz means of spectral functions and eigenfunction expansion for elliptic differential operators, Lecture at the Belfer Graduate School. Preprint, Yeshiva University, 1966 | MR

[16] Alimov Sh. A., “Drobnye stepeni ellipticheskikh operatorov i izomorfizm klassov differentsiruemykh funktsii”, Differents. uravneniya, 8:9 (1972), 1609–1626 | MR | Zbl