Using the notions of frame transform and of square integrable projective representation of a locally compact group G, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier Hilbert space of the representation into the space of square integrable functions on the direct product group G × G. These transforms have remarkable properties...

This paper presents a Hilbert transform method for pricing Bermudan options in Lévy models. The corresponding optimal stopping problem is reduced to a backward induction in the Fourier space that involves taking Hilbert transforms of certain analytic functions or integrating such functions. The Hilbert transforms and integrals can be discretized using very simple schemes. The resulting discrete...

Abstract The goal of the paper is to obtain analogs sampling theorems and Riesz–Boas interpolation formulas which are relevant discrete Hilbert Kak–Hilbert transforms in $l^{2}$ .

We describe the structure of resolvent discrete rough truncated Hilbert transform under critical exponent. This extends our results obtained in [Ann. Scuola Norm. Sup. Pisa 19 (2019)].