An Integral Representation for the Product of Spectral Measures

1 January 1968

journal article
Published by Canadian Mathematical Society in Canadian Journal of Mathematics

Vol. 20, 904-912
https://doi.org/10.4153/cjm-1968-087-0

Abstract

Let be a Hilbert space with inner product (•, •) and let E(•) and E⁰(•) be spectral measures in corresponding to self-adjoint operators and . In this paper we consider the set function ƒ(I × J) = E(I)E⁰(J) defined on the semiring of bounded rectangles, and obtain an integral representation for this set function for disjoint I, J under the hypotheses that H — H₀ is a type of Carleman operator.

Keywords

PRODUCT OF SPECTRAL MEASURES
INTEGRAL REPRESENTATION FOR THE PRODUCT

This publication has 1 reference indexed in Scilit:

Eindeutige Analytische Funktionen
Published by Springer Nature ,1936