2025/03/27 by Abtin Daghighi, Daghighi, Abtin
Mathematics · #30G30 #32A30 #32W50 #35G05 #35J30 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2503.21909
openalex publication_date 2025/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Brief Description: The book provides a unique highly self-contained text introducing the reader to the classical and modern theory of polyanalytic functions and their generalizations. This is a subbranch of complex analysis of several variables, in particular polyanalytic functions where introduced as a natural generalization of holomorphic functions. The book includes a solid treatment of the most important well-known results from the inception of the subspecialty, but also covers a wide variety of generalizations and recent developments which have arisen since the latest monograph on the subject was published. A careful selection has been made of topics and results to include, in order to provide the reader with a classic repertoire and a modern overview. The style and presentation is old-school and rigorous and the author does not shy away from presenting complete proofs also for important theorems which require involved background for a modern demonstration.