The Mittag-Leffler Bargmann Transform

Natanael Alpay and Kamal Diki

Published research

Research Summary

We construct and investigate a Mittag-Leffler version of the Segal–Bargmann transform. The work relates the transform to Fourier analysis and studies creation and annihilation operators involving fractional differentiation.

We also develop a quaternionic extension in the slice-hyperholomorphic setting, connecting complex and hypercomplex function-space methods.

Published article Preprint on arXiv

Publication Details

N. Alpay and K. Diki. On the Mittag Leffler Bargmann (MLB) transform. Journal of Mathematical Analysis and Applications 527 (2023), no. 2, article 127458.