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Some examples related to Kato's conjecture

Part of: Special classes of linear operators Elliptic equations and systems

Published online by Cambridge University Press:  09 April 2009

Rhonda J. Hughes  and
Paul R. Chernoff
Rhonda J. Hughes
Affiliation:
Department of MathematicsBryn Mawr CollegeBryn Mawr, PA 19010USA e-mail: rhughes@cc.brynmawr.edu
Paul R. Chernoff
Affiliation:
Depratment of MathematicsUniversity of California, Berkeley Berkeley, CA 94720USA e-mail: chernoff@math.berkeley.edu
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Abstract

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We show that the Kato conjecture is true for m-accretive operators with highly singular coefficients. For operators of the form A = *F, where formally corresponds to d/dx + zδ on L2 (R), we prove that Dom (A1/2) = Dom() = e-zHH1(R) where H is the Heavysied function. By adapting recent methods of Auscher and Tchamitchian, we characterize Dom (A) in terms of an unconditional wavelet basis for L2(R).

MSC classification

Secondary: 47B25: Symmetric and selfadjoint operators (unbounded) 47B44: Accretive operators, dissipative operators, etc. 35J15: Second-order elliptic equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 2 , April 1996 , pp. 274 - 286
Copyright
Copyright © Australian Mathematical Society 1996

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