IJPAM: Volume 54, No. 3 (2009)

INTEGRAL REPRESENTATIONS OF UNBOUNDED
OPERATORS BY INFINITELY SMOOTH
BI-CARLEMAN KERNELS

Igor M. Novitskii
Institute for Applied Mathematics
Far-Eastern Branch of the Russian Academy of Sciences
Dzerzhinskiy Street 54, Khabarovsk, 680 000, RUSSIA
e-mail: novim@iam.khv.ru

Abstract.In this paper, we establish that if a closed linear operator in a separable Hilbert space is unitarily equivalent to a bi-Carleman integral operator in an appropriate , then that operator is unitarily equivalent to a bi-Carleman integral operator in , whose kernel and two Carleman functions , are infinitely smooth and vanish at infinity together with all partial and all strong derivatives, respectively. The implementing unitary operator (from onto ) is found by direct construction.

Received: June 6, 2009

AMS Subject Classification: 47G10, 45P05, 47B33, 47B38

Key Words and Phrases: closed linear operator, integral linear operator, Carleman integral operator, bi-Carleman integral operator, characterization theorems for integral operators, linear integral equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 3