Izvorni znanstveni članak

https://doi.org/10.3336/gm.60.1.07

The Laplace transform on the cones of lattice-structured Banach spaces

Diana Hunjak orcid.org/0009-0007-7597-8395 ; Faculty of Transport and Traffic Sciences, University of Zagreb, 10 000 Zagreb, Croatia

Preuzmi JATS datoteku

Sažetak

Characterizations of positive definite functions defined on convex cones using the Laplace transform of a measure are commonly referred to as Nussbaum-type theorems. This paper establishes a Nussbaum-type theorem in the context where the domain of a \(B(\mathcal{H})\)-valued positive definite function is a positive cone within a Banach space that is also a vector lattice, but not necessarily a Banach lattice. Such spaces include examples like Sobolev spaces \(W^{1,p}(\Omega)\). Utilizing the Berg-Maserick theorem, we prove that the unique representing measure is Radon measure concentrated on a subset of the topological dual.

Ključne riječi

Positive definite function, integral representation, Laplace transform, \(\alpha\)-boundedness, Banach lattice.

Hrčak ID:

332471

URI

https://hrcak.srce.hr/332471

Datum izdavanja:

6.3.2026.

Posjeta: 346 *