TY - CHAP
T1 - Quaternionic Hilbert Spaces and Slice Hyperholomorphic Functions
AU - Alpay, Daniel
AU - Colombo, Fabrizio
AU - Sabadini, Irene
N1 - Publisher Copyright:
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
PY - 2024/1/1
Y1 - 2024/1/1
N2 - The purpose of the present book is to develop the counterparts of Banach and Hilbert spaces in the setting of slice hyperholomorphic functions. Banach and Hilbert spaces of analytic functions, in one or several complex variables, play an important role in analysis and related fields. Besides their intrinsic interest, such spaces have numerous applications. The book is divided into three parts. In the first part, some foundational material on quaternionic functions and functional analysis are introduced. The second part is the core of the book and contains various types of functions spaces ranging from the Hardy spaces, also in the fractional case, to the Fock space extended to the case of quaternions. The third and final part present some further generalization. Researchers in functional analysis and hypercomplex analysis will find this book a key contribution to their field, but also researchers in mathematical physics, especially in quantum mechanics, will benefit from the insights presented.
AB - The purpose of the present book is to develop the counterparts of Banach and Hilbert spaces in the setting of slice hyperholomorphic functions. Banach and Hilbert spaces of analytic functions, in one or several complex variables, play an important role in analysis and related fields. Besides their intrinsic interest, such spaces have numerous applications. The book is divided into three parts. In the first part, some foundational material on quaternionic functions and functional analysis are introduced. The second part is the core of the book and contains various types of functions spaces ranging from the Hardy spaces, also in the fractional case, to the Fock space extended to the case of quaternions. The third and final part present some further generalization. Researchers in functional analysis and hypercomplex analysis will find this book a key contribution to their field, but also researchers in mathematical physics, especially in quantum mechanics, will benefit from the insights presented.
KW - Frechet Spaces
KW - Quaternionic Functions
KW - Quaternionic Linear Operator
KW - Quaternionic Stochastic Processes
KW - Reproducing Kernel Hilbert Spaces
KW - Slice Poly-Hyperholomorphic Functions
UR - https://www.scopus.com/pages/publications/85216988200
U2 - 10.1007/978-3-031-73430-4
DO - 10.1007/978-3-031-73430-4
M3 - Chapter
AN - SCOPUS:85216988200
T3 - Operator Theory: Advances and Applications
SP - 1
EP - 343
BT - Operator Theory
PB - Springer Science and Business Media Deutschland GmbH
ER -