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Square Laplacian perturbed by inverse fourth-power potential. I Self-adjointness (real case)

Published online by Cambridge University Press:  04 April 2011

Noboru Okazawa ,
Hiroshi Tamura  and
Tomomi Yokota
Noboru Okazawa
Affiliation:
Department of Mathematics, Science University of Tokyo, Kagurazaka 1–3, Shinjuku-ku, Tokyo 162-8601, Japanokazawa@ma.kagu.tus.ac.jp
Hiroshi Tamura
Affiliation:
Department of Mathematics, Science University of Tokyo, Kagurazaka 1–3, Shinjuku-ku, Tokyo 162-8601, Japanhi-ro-shi@u01.gate01.com
Tomomi Yokota
Affiliation:
Department of Mathematics, Science University of Tokyo, Kagurazaka 1–3, Shinjuku-ku, Tokyo 162-8601, Japanyokota@rs.kagu.tus.ac.jp
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Abstract

The self-adjointness of Δ2 + κ|x|−4 (κ>κ0 = κ0(N)) in L2(ℝN) is established as an application of the perturbation theorem in terms of Re(Au, Bεu), u ∈ D(A), for two non-negative self-adjoint operators A, B in a Hilbert space, where the family {Bε}ε>0 is the Yosida approximation of B. A key to the proof lies in a new inequality for the functions ν ∈ L2(ℝN) with |x|2Δν ∈ L2(ℝN) derived by using two real parameters.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 2 , April 2011 , pp. 409 - 416
Copyright
Copyright © Royal Society of Edinburgh 2011

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