Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 991–1002

CHARACTERIZING COMPACT FAMILIES VIA THE LAPLACE TRANSFORM

Mateusz Krukowski

Lódź University of Technology, Institute of Mathematics
Wólczańska 215, 90-924 Lódź, Poland; krukowski.mateusz13 'at' gmail.com

Abstract. In 1985, Pego characterized compact families in L²(R) in terms of the Fourier transform. It took nearly 30 years to realize that Pego's result can be proved in a more general setting of locally compact abelian groups (works of Górka and Kostrzewa). In the current paper, we argue that the Fourier transform is not the only integral transform that is efficient in characterizing compact families and suggest the Laplace transform as a possible alternative.

2010 Mathematics Subject Classification: Primary 44A10, 42A38.

Key words: Laplace transform, Pego theorem, compactness.

Reference to this article: M. Krukowski: Characterizing compact families via the Laplace transform. Ann. Acad. Sci. Fenn. Math. 45 (2020), 991–1002.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4553