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Sectorial forms and unbounded subnormals

Published online by Cambridge University Press:  01 November 2007

AMEER ATHAVALE  and
SAMEER CHAVAN
AMEER ATHAVALE
Affiliation:
Department of Mathematics, Indian Institute of Technology Bombay, Mumbai 400076, India. email: athavale@math.iitb.ac.in
SAMEER CHAVAN
Affiliation:
Department of Mathematics, University of Pune, Pune 411007, India. e-mail: chavansameer@gmail.com
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Abstract

We use the theory of sectorial sesquilinear forms to characterize the closure of the Creation Operator of Quantum Mechanics in the classical set-up. Further, we bring that theory to bear upon the class of unbounded cyclic subnormal operators that admit analytic models; in particular, we provide a sufficient condition for the existence of complete sets of eigenvectors for certain sectorial operators related to unbounded subnormals. The relevant theory is illustrated in the context of a class of analytic models of which the classical Segal–Bargmann space is a prototype. The framework of sectorial sesquilinear forms is also shown to be specially useful for treating questions related to the existence, uniqueness and stability of certain parabolic evolution equations naturally associated with such analytic models.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 3 , November 2007 , pp. 685 - 702
Copyright
Copyright © Cambridge Philosophical Society 2007

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