# Spectrum of the weighted Laplace operator in unbounded domains

Mathematica Bohemica (2011)

- Volume: 136, Issue: 4, page 415-427
- ISSN: 0862-7959

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topFilinovskiy, Alexey. "Spectrum of the weighted Laplace operator in unbounded domains." Mathematica Bohemica 136.4 (2011): 415-427. <http://eudml.org/doc/196401>.

@article{Filinovskiy2011,

abstract = {We investigate the spectral properties of the differential operator $-r^s \Delta $, $s\ge 0$ with the Dirichlet boundary condition in unbounded domains whose boundaries satisfy some geometrical condition. Considering this operator as a self-adjoint operator in the space with the norm $\Vert u\Vert ^2_\{L_\{2, s\} (\Omega )\}= \int _\{\Omega \} r^\{-s\} |u|^2 \{\rm d\} x $, we study the structure of the spectrum with respect to the parameter $s$. Further we give an estimate of the rate of condensation of discrete spectra when it changes to continuous.},

author = {Filinovskiy, Alexey},

journal = {Mathematica Bohemica},

keywords = {Laplace operator; multiplicative perturbation; Dirichlet problem; Friedrichs extension; purely discrete spectra; purely continuous spectra; weighted Laplace operator; Friedrichs extension; purely discrete spectra; purely continuous spectra},

language = {eng},

number = {4},

pages = {415-427},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Spectrum of the weighted Laplace operator in unbounded domains},

url = {http://eudml.org/doc/196401},

volume = {136},

year = {2011},

}

TY - JOUR

AU - Filinovskiy, Alexey

TI - Spectrum of the weighted Laplace operator in unbounded domains

JO - Mathematica Bohemica

PY - 2011

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 136

IS - 4

SP - 415

EP - 427

AB - We investigate the spectral properties of the differential operator $-r^s \Delta $, $s\ge 0$ with the Dirichlet boundary condition in unbounded domains whose boundaries satisfy some geometrical condition. Considering this operator as a self-adjoint operator in the space with the norm $\Vert u\Vert ^2_{L_{2, s} (\Omega )}= \int _{\Omega } r^{-s} |u|^2 {\rm d} x $, we study the structure of the spectrum with respect to the parameter $s$. Further we give an estimate of the rate of condensation of discrete spectra when it changes to continuous.

LA - eng

KW - Laplace operator; multiplicative perturbation; Dirichlet problem; Friedrichs extension; purely discrete spectra; purely continuous spectra; weighted Laplace operator; Friedrichs extension; purely discrete spectra; purely continuous spectra

UR - http://eudml.org/doc/196401

ER -

## References

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