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Mat. Zametki, 1977, Volume 22, Issue 5, Pages 679–698 (Mi mz8092)  

This article is cited in 14 scientific papers (total in 14 papers)

Convergence of eigenfunction expansions at points of discontinuity of the coefficients of a differential operator

V. A. Il'in

M. V. Lomonosov Moscow State University

Abstract: The question of the convergence of expansions in the eigenfunctions of a differential operator with discontinuous coefficients at a point $x_0$ of discontinuity of the coefficients is studied. Given an arbitrary function $f(x)$ in the class $L_2$, a corresponding function $\widetilde f_{x_0}(x)$ is constructed which is such that at the point $x_0$ the eigenfunction expansion of $f(x)$ diverges with the expansion of $\widetilde f_{x_0}(x)$ into a Fourier trigonometric series.

Full text: PDF file (1299 kB)

English version:
Mathematical Notes, 1977, 22:5, 870–882

Bibliographic databases:

UDC: 517.4
Received: 18.04.1977

Citation: V. A. Il'in, “Convergence of eigenfunction expansions at points of discontinuity of the coefficients of a differential operator”, Mat. Zametki, 22:5 (1977), 679–698; Math. Notes, 22:5 (1977), 870–882

Citation in format AMSBIB
\Bibitem{Ili77}
\by V.~A.~Il'in
\paper Convergence of eigenfunction expansions at points of discontinuity of the coefficients of a~differential operator
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 5
\pages 679--698
\mathnet{http://mi.mathnet.ru/mz8092}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=499820}
\zmath{https://zbmath.org/?q=an:0364.34011}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 5
\pages 870--882
\crossref{https://doi.org/10.1007/BF01098352}


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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. S. I. Mitrokhin, “Ob asimptotike sobstvennykh znachenii modelnoi kraevoi zadachi dlya semeistva differentsialnykh operatorov s summiruemym potentsialom”, Mezhdunar. nauch.-issled. zhurn., 2016, no. 10-2(52), 137–143  mathnet  crossref
    2. S. I. Mitrokhin, “Ob issledovanii spektra kraevoi zadachi dlya differentsialnogo operatora pyatogo poryadka s summiruemym potentsialom”, Matematicheskie zametki SVFU, 23:2 (2016), 78–89  mathnet  elib
    3. S. I. Mitrokhin, “Mnogotochechnye differentsialnye operatory: rasscheplenie kratnykh v glavnom sobstvennykh znachenii”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 17:1 (2017), 5–18  mathnet  crossref  elib
    4. S. I. Mitrokhin, “Ob effekte rasschepleniya dlya mnogotochechnykh differentsialnykh operatorov s summiruemym potentsialom”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:2 (2017), 249–270  mathnet  crossref  zmath  elib
    5. S. I. Mitrokhin, “Study of differential operator with summable potential and discontinuous weight function”, Ufa Math. J., 9:4 (2017), 72–84  mathnet  crossref  isi  elib
    6. S. I. Mitrokhin, “Spectral properties of the family of even order differential operators with a summable potential”, Moscow University Mathematics Bulletin, 72:4 (2017), 137–148  mathnet  crossref  mathscinet  isi  elib
    7. S. I. Mitrokhin, “Asymptotics of spectrum of multipoint differential operators with summable potential”, J. Math. Sci., 231:2 (2018), 243–254  mathnet  crossref  crossref
    8. S. I. Mitrokhin, “Asymptotic of eigenvalues of differential operator with alternating weight function”, Russian Math. (Iz. VUZ), 62:6 (2018), 27–42  mathnet  crossref  isi
    9. S. I. Mitrokhin, “Asymptotics of eigenvalues of fourth order differential operator with alternating weight function”, Moscow University Mathematics Bulletin, 73:6 (2018), 254–265  mathnet  crossref  mathscinet  zmath  isi
    10. S. I. Mitrokhin, “Asimptotika spektra semeistva funktsionalno-differentsialnykh operatorov s summiruemym potentsialom”, Sib. zhurn. chist. i prikl. matem., 18:4 (2018), 56–80  mathnet  crossref
    11. S. I. Mitrokhin, “O spektralnykh svoistvakh semeistva differentsialnogo operatora chetnogo poryadka s summiruemym potentsialom”, Matematicheskaya fizika i kompyuternoe modelirovanie, 21:2 (2018), 13–26  mathnet  crossref
    12. I. S. Lomov, “Spektralnyi metod Ilina ustanovleniya svoistv bazisnosti i ravnomernoi skhodimosti biortogonalnykh razlozhenii na konechnom intervale”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 19:1 (2019), 34–58  mathnet  crossref  elib
    13. S. I. Mitrokhin, “Asimptotika spektra differentsialnogo operatora chetnogo poryadka s razryvnoi vesovoi funktsiei”, Zhurnal SVMO, 22:1 (2020), 48–70  mathnet  crossref
    14. S. I. Mitrokhin, “Ob asimptotike spektra differentsialnogo operatora chetnogo poryadka, potentsialom kotorogo yavlyaetsya delta-funktsiya”, Zhurnal SVMO, 22:3 (2020), 280–305  mathnet  crossref
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