The work is dedicated to investigating a limiting procedure for extending “local” integral operator equalities to “global” ones in the sense explained below, and to applying it to obtaining generalizations of the Newton-Leibniz formula for operator-valued functions for a wide class of unbounded operators. The integral equalities considered have the form . (1) They involve functions of the kind , where X is a general locally compact space, F runs over a suitable class of Banach subspaces of a fixed complex Banach space G, in particular F = G. The integrals are with respect to a general complex Radon measure on X and the -topology on B(F), where is a suitable subset of B(F)*, the topological dual of B(F). is a possibly unbounded scalar type spectral operator in F such that , and for all x ∈ X, and g,h are complex-valued Borelian maps on the spectrum of . If F ≠ G we call the integral equality (1) “local”, while if F = G we call it “global”.
@book{bwmeta1.element.bwnjournal-rm-doi-10_4064-dm464-0-1, author = {Benedetto Silvestri}, title = {Integral equalities for functions of unbounded spectral operators in Banach spaces}, series = {GDML\_Books}, year = {2009}, zbl = {1235.47035}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm464-0-1} }
Benedetto Silvestri. Integral equalities for functions of unbounded spectral operators in Banach spaces. GDML_Books (2009), http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm464-0-1/