Sectorial forms and unbounded subnormals

• Autores: Ameer Athavale, Sameer Chavan
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 143, Nº 3, 2007, págs. 685-702
• Idioma: inglés
• DOI: 10.1017/s0305004107000552
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• Resumen

  • 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.