My main interest are different types of spectral
asymptotics and estimates for partial differential
and some ordinary differential operators.
- Estimates of singular values
for resolvent powers differences and semigroups differences.
- Asymptotics of the ground state with respect to a small parameter.
- Asymptotics of negative spectra for lower unbounded
operators.
Also I am interested in pathological spectral properties
of Schrödinger operators with potentials supported on null measure sets
such as purely singular continuous spectrum or embedded eigenvalues.
Submitted papers: |
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- Vladimir Lotoreichik and Sergey Simonov,
Spectral analysis of the Kronig-Penney model with Wigner-von Neumann perturbations,
submitted
- Jussi Behrndt, Matthias Langer and Vladimir Lotoreichik,
Schrödinger operators with delta and delta'-potentials supported on hypersurfaces,
submitted
- Jussi Behrndt, Matthias Langer and Vladimir Lotoreichik,
Spectral estimates for resolvent differences of self-adjoint elliptic operators
submitted
Published papers: |
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- Vladimir Lotoreichik and Jonathan Rohleder
Schatten-von Neumann estimates
for resolvent differences of Robin Laplacians on a half-space,
Operator Theory: Advances and Applications, 221 (2012), 471--486.
- Vladimir Lotoreichik
Singular continuous spectrum of half-line Schrödinger operators with point interactions on a sparse set,
Opuscula Math., 31 (2011), 615--628.
- Jussi Behrndt, Matthias Langer, Igor Lobanov, Vladimir Lotoreichik and Igor Yu. Popov,
A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains,
J. Math. Anal. Appl., 371 (2010), 750--758.
- Igor Lobanov, Vladimir Lotoreichik and Igor Yu. Popov,
Lower bound on the spectrum of the Schrödinger operator in the plane with delta-potential supported by a curve,
Theor. Math. Phys., 162 (2010), 332--340.
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