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Full-Text Articles in Mathematics
Fock And Hardy Spaces: Clifford Appell Case, Daniel Alpay, Kamal Diki, Irene Sabadini
Fock And Hardy Spaces: Clifford Appell Case, Daniel Alpay, Kamal Diki, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we study a specific system of Clifford–Appell polynomials and, in particular, their product. Moreover, we introduce a new family of quaternionic reproducing kernel Hilbert spaces in the framework of Fueter regular functions. The construction is based on a general idea which allows us to obtain various function spaces by specifying a suitable sequence of real numbers. We focus on the Fock and Hardy cases in this setting, and we study the action of the Fueter mapping and its range.
On The Global Operator And Fueter Mapping Theorem For Slice Polyanalytic Functions, Daniel Alpay, Kamal Diki, Irene Sabadini
On The Global Operator And Fueter Mapping Theorem For Slice Polyanalytic Functions, Daniel Alpay, Kamal Diki, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we prove that slice polyanalytic functions on quaternions can be considered as solutions of a power of some special global operator with nonconstant coefficients as it happens in the case of slice hyperholomorphic functions. We investigate also an extension version of the Fueter mapping theorem in this polyanalytic setting. In particular, we show that under axially symmetric conditions it is always possible to construct Fueter regular and poly-Fueter regular functions through slice polyanalytic ones using what we call the poly-Fueter mappings. We study also some integral representations of these results on the quaternionic unit ball.
Wiener Algebra For The Quaternions, Daniel Alpay, Fabrizio Colombo, David P. Kimsey, Irene Sabadini
Wiener Algebra For The Quaternions, Daniel Alpay, Fabrizio Colombo, David P. Kimsey, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-Lévy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener-Hopf operators.