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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2002, Volume 236, Pages 262–271 (Mi tm296)  
This article is cited in 3 scientific papers (total in 3 papers)

Schrödinger Operators with Singular Potentials

M. I. Neiman-Zade, A. M. Savchuk

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (199 kB) Citations (3)
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Abstract: Schrödinger operators are investigated whose potentials represent generalized functions. A problem of physically correct determination of such operators is solved by two different methods in the case of one and several variables. In the first case, the potential must represent an element of the negative space $W^{-1}_2$; then, the operator obtained can be analyzed in greater detail. In the second case, a requirement is imposed on the potential that it must belong to the class of multipliers from $W^{1}_2$ to $W^{-1}_2$. In addition, the space of multipliers is analyzed.
Received in December 2000
Bibliographic databases:
UDC: 517.9+517.43
Language: Russian
Citation: M. I. Neiman-Zade, A. M. Savchuk, “Schrödinger Operators with Singular Potentials”, Differential equations and dynamical systems, Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko, Trudy Mat. Inst. Steklova, 236, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 262–271; Proc. Steklov Inst. Math., 236 (2002), 250–259
Citation in format AMSBIB
\Bibitem{NeiSav02}
\by M.~I.~Neiman-Zade, A.~M.~Savchuk
\paper Schr\"odinger Operators with Singular Potentials
\inbook Differential equations and dynamical systems
\bookinfo Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko
\serial Trudy Mat. Inst. Steklova
\yr 2002
\vol 236
\pages 262--271
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm296}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1931026}
\zmath{https://zbmath.org/?q=an:1020.34081}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2002
\vol 236
\pages 250--259
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