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Mat. Zametki, 2002, Volume 71, Issue 5, Pages 643–651 (Mi mz373)  

This article is cited in 18 scientific papers (total in 18 papers)

Multipliers in Dual Sobolev Spaces and Schrödinger Operators with Distribution Potentials

A. A. Shkalikova, J.-G. Bak

a M. V. Lomonosov Moscow State University

Abstract: Certain sufficient conditions for functions to be embedded in the space of multipliers from the Sobolev space $H^\alpha _p({\mathbb R}^n)$ to the dual space $H^{-\alpha }_{p'}({\mathbb R}^n)$ are obtained in the present paper. In the case $\alpha >n/p$ a criterion is found, i.e., a precise description of these spaces of multipliers is given. The obtained results are applied to define the Schödinger operator with distribution potentials.

DOI: https://doi.org/10.4213/mzm373

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English version:
Mathematical Notes, 2002, 71:5, 587–594

Bibliographic databases:

UDC: 517.983
Received: 30.10.2001

Citation: A. A. Shkalikov, J. Bak, “Multipliers in Dual Sobolev Spaces and Schrödinger Operators with Distribution Potentials”, Mat. Zametki, 71:5 (2002), 643–651; Math. Notes, 71:5 (2002), 587–594

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
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    2. Neiman-Zade, MI, “Strongly elliptic operators with singular coefficients”, Russian Journal of Mathematical Physics, 13:1 (2006), 70  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Hryniv, RO, “Eigenvalue asymptotics for Sturm-Liouville operators with singular potentials”, Journal of Functional Analysis, 238:1 (2006), 27  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Yu. V. Pokornyi, M. B. Zvereva, S. A. Shabrov, “Sturm–Liouville oscillation theory for impulsive problems”, Russian Math. Surveys, 63:1 (2008), 109–153  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. Djakov P., Mityagin B., “Spectral gaps of Schrodinger operators with periodic singular potentials”, Dyn Partial Differ Equ, 6:2 (2009), 95–165  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. Djakov P., Mityagin B., “Fourier Method for One-Dimensional Schrodinger Operators with Singular Periodic Potentials”, Topics in Operator Theory, Vol 2: Systems and Mathematical Physics, Operator Theory Advances and Applications, 203, eds. Ball J., Bolotnikov V., Helton J., Rodman L., Spitkovsky I., Birkhauser Verlag Ag, 2010, 195–236  crossref  mathscinet  isi
    7. A. I. Parfenov, “A characterization of multipliers in the Hedberg–Netrusov spaces”, Siberian Adv. Math., 22:1 (2012), 13–40  mathnet  crossref  mathscinet  elib
    8. V. A. Mikhailets, V. M. Molyboga, “On the Spectrum of Singular Perturbations of Operators on the Circle”, Math. Notes, 91:4 (2012), 588–591  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    9. Gesztesy F., Weikard R., “Some Remarks on the Spectral Problem Underlying the Camassa-Holm Hierarchy”, Operator Theory in Harmonic and Non-Commutative Analysis, Operator Theory Advances and Applications, 240, eds. Ball J., Dritschel M., TerElst A., Portal P., Potapov D., Birkhauser Verlag Ag, 2014, 137–188  crossref  mathscinet  zmath  isi
    10. Eckhardt J., Gesztesy F., Nichols R., Teschl G., “Supersymmetry and Schrodinger-Type Operators With Distributional Matrix-Valued Potentials”, J. Spectr. Theory, 4:4 (2014), 715–768  crossref  mathscinet  zmath  isi  scopus  scopus
    11. I. V. Tsylin, “On the Regularity of Solutions of Variational and Boundary-Value Problems in Domains with Hölder Boundary”, Math. Notes, 99:5 (2016), 785–791  mathnet  crossref  crossref  mathscinet  isi  elib
    12. L. K. Kusainova, A. Myrzagaliyeva, Ya. T. Sultanaev, “On the Boundedness of the Schrödinger Operator in Weighted Sobolev Spaces”, Math. Notes, 99:6 (2016), 948–953  mathnet  crossref  crossref  mathscinet  isi  elib
    13. J. V. Tikhonov, I. A. Sheipak, “On the string equation with a singular weight belonging to the space of multipliers in Sobolev spaces with negative index of smoothness”, Izv. Math., 80:6 (2016), 1242–1256  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    14. I. V. Tsylin, “Regularity of solutions to Dirichlet boundary value problem in domains on a manifold”, Moscow University Mathematics Bulletin, 71:5 (2016), 204–207  mathnet  crossref  mathscinet  isi
    15. A. A. Belyaev, A. A. Shkalikov, “Multipliers in Spaces of Bessel Potentials: The Case of Indices of Nonnegative Smoothness”, Math. Notes, 102:5 (2017), 632–644  mathnet  crossref  crossref  mathscinet  isi  elib
    16. A. A. Belyaev, A. A. Shkalikov, “Multipliers in Bessel potential spaces: the case of smoothness indices of different sign”, St. Petersburg Math. J., 30:2 (2019), 203–218  mathnet  crossref  mathscinet  isi  elib
    17. V. D. Stepanov, E. P. Ushakova, “Hardy–Steklov Operators and the Duality Principle in Weighted First-Order Sobolev Spaces on the Real Axis”, Math. Notes, 105:1 (2019), 91–103  mathnet  crossref  crossref  mathscinet  isi  elib
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