IJPAM: Volume 50, No. 2 (2009)

UNITARY EQUIVALENCE TO INTEGRAL
OPERATORS AND AN APPLICATION

Igor M. Novitski{\u{\i\/}}\kern.15em
Institute for Applied Mathematics
Far Eastern Branch of the Russian Academy of Sciences
54, Dzerzhinski Str., Khabarovsk, 680 000, RUSSIA
e-mail: novim@iam.khv.ru


Abstract.In this paper, we characterize all closed, linear, densely defined operators in a separable Hilbert space which are unitarily equivalent to a Carleman integral operator in $L^2(\mathbb{R})$ whose kernel and Carleman functions are infinitely smooth and vanish at infinity together with all derivatives. There is an application to third-kind integral equations.

Received: August 14, 2008

AMS Subject Classification: 47B38, 47G10

Key Words and Phrases: Carleman kernel, characterization theorems for integral operators, integral linear equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 2