An Lp theory for Schrödinger operators with nonnegative potentials

Noboru OKAZAWA

doi:10.2969/jmsj/03640675

An L^p theory for Schrödinger operators with nonnegative potentials

Noboru OKAZAWA

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1984 Volume 36 Issue 4 Pages 675-688

DOI https://doi.org/10.2969/jmsj/03640675

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Published: 1984 Received: November 17, 1983 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R. A. Adams, Sobolev spaces, Pure and Applied Math., 65, Academic Press, New York, 1975.
2) W. D. Evans and A. Zettl, Dirichlet and separation results for Schrödinger-type operators, Proc. Roy. Soc. Edinburgh Sect. A, 80 (1978), 151-162.
3) W. N. Everitt and M. Giertz, Inequalities and separation for Schrödinger type operators in L₂(Rⁿ), Proc. Roy. Soc. Edinburgh Sect. A, 79 (1977), 257-265.
4) W. G. Faris, Selfadjoint operators, Lecture Notes in Math., 433, Springer-Verlag, 1975.
5) T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19 (1967), 508-520.
6) T. Kato, Schrödinger operators with singular potentials, Israel J. Math., 13 (1972), 135-148.
7) T. Kato, Remarks on the selfadjointness and related problems for differential operators, Spectral theory of differential operators, Math. Studies, 55, North-Holland, Amsterdam and New York, 1981, 253-266.
8) S. T. Kuroda, Spectral theory II, Iwanami-Shoten, Tokyo, 1979 (in Japanese).
9) G. Lumer and R. S. Phillips, Dissipative operators in a Banach space, Pacific J. Math., 11 (1961), 679-698.
10) N. Okazawa, Singular perturbations of m-accretive operators, J. Math. Soc. Japan, 32 (1980), 19-44.
11) N. Okazawa, On the perturbation of linear operators in Banach and Hilbert spaces, J. Math. Soc. Japan, 34 (1982), 677-701.
12) M. Reed and B. Simon, Methods of modern mathematical physics, Vol. II, Fourier analysis, selfadjointness, Academic Press, New York, 1975.
13) M. Reed and B. Simon, Methods of modern mathematical physics, Vol. IV, Analysis of operators, Academic Press, New York, 1978.
14) M. Schechter, Spectra of partial differential operators, Applied Math. and Mechanics, 14, North-Holland, Amsterdam, 1971.
15) Yu. A. Semenov, Schrödinger operators with L^p_loc-potentials, Comm. Math. Phys., 53(1977), 277-284.
16) H. Sohr, Störungstheoretische Regularitätsuntersuchungen, Math. Z., 179 (1982), 179-192.
17) H. Tanabe, Equation of evolution, Monographs and Studies in Math., 6, Pitman, London, 1979.
18) K. Yosida, Functional analysis, Die Grundlehren der math. Wissenschaften, 123, Springer-Verlag, Berlin and New York, 1965; 5th ed., 1978.

Right : [1] R. A. Adams, Sobolev spaces, Pure and Applied Math., 65, Academic Press, New York, 1975.
[2] W. D. Evans and A. Zettl, Dirichlet and separation results for Schrödinger-type operators, Proc. Roy. Soc. Edinburgh Sect. A, 80 (1978), 151-162.
[3] W. N. Everitt and M. Giertz, Inequalities and separation for Schrödinger type operators in L₂(Rⁿ), Proc. Roy. Soc. Edinburgh Sect. A, 79 (1977), 257-265.
[4] W. G. Faris, Selfadjoint operators, Lecture Notes in Math., 433, Springer-Verlag, 1975.
[5] T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19 (1967), 508-520.
[6] T. Kato, Schrödinger operators with singular potentials, Israel J. Math., 13 (1972), 135-148.
[7] T. Kato, Remarks on the selfadjointness and related problems for differential operators, Spectral theory of differential operators, Math. Studies, 55, North-Holland, Amsterdam and New York, 1981, 253-266.
[8] S. T. Kuroda, Spectral theory II, Iwanami-Shoten, Tokyo, 1979 (in Japanese).
[9] G. Lumer and R. S. Phillips, Dissipative operators in a Banach space, Pacific J. Math., 11 (1961), 679-698.
[10] N. Okazawa, Singular perturbations of m-accretive operators, J. Math. Soc. Japan, 32 (1980), 19-44.
[11] N. Okazawa, On the perturbation of linear operators in Banach and Hilbert spaces, J. Math. Soc. Japan, 34 (1982), 677-701.
[12] M. Reed and B. Simon, Methods of modern mathematical physics, Vol. II, Fourier analysis, selfadjointness, Academic Press, New York, 1975.
[13] M. Reed and B. Simon, Methods of modern mathematical physics, Vol. IV, Analysis of operators, Academic Press, New York, 1978.
[14] M. Schechter, Spectra of partial differential operators, Applied Math. and Mechanics, 14, North-Holland, Amsterdam, 1971.
[15] Yu. A. Semenov, Schrödinger operators with L^p_loc-potentials, Comm. Math. Phys., 53 (1977), 277-284.
[16] H. Sohr, Störungstheoretische Regularitätsuntersuchungen, Math. Z., 179 (1982), 179-192.
[17] H. Tanabe, Equation of evolution, Monographs and Studies in Math., 6, Pitman, London, 1979.
[18] K. Yosida, Functional analysis, Die Grundlehren der math. Wissenschaften, 123, Springer-Verlag, Berlin and New York, 1965; 5th ed., 1978.

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