02876nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001200172072001700184072002300201072001600224100008900240245008700329250001800416264007300434300003400507336002600541337002600567338003600593347002400629490006600653505056600719520058901285650004301874650002101917650005801938650002101996650004402017710003402061773002602095776003602121776003602157776003602193830007302229856004602302912001402348912001502362999001702377978-3-031-76181-2DE-He21320251030114912.0cr nn 008mamaa241231s2024    sz |    s    |||| 0|eng d  a97830317618129978-3-031-76181-27 a10.1007/978-3-031-76181-22doi 4aQA331.7 7aPBKD2bicssc 7aMAT0340002bisacsh 7aPBKD2thema1 aVasilevski, Nikolai.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98995510aPolyanalytic Type Function Spacesh[electronic resource] /cby Nikolai Vasilevski.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Birkhäuser,c2024.  aXXX, 174 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aOperator Theory: Advances and Applications,x2296-4878 ;v3050 aForeword -- Preface -- Introduction -- I Spaces of polyanalytic type in one complex variable -- 1 Extended Fock-space construction approach -- 2 Complex plane C case -- 3 Unit disk D case -- 4 Upper half-plane Π case -- 5 Basis oriented approach -- 6 Approach based on pure isometries -- II Spaces of polyanalytic type in several complex variables -- 7 Multi-operator extended Fock-space construction -- 8 The Cn case -- 9 The unit ball Bn case -- 10 Hilbert spaces with generalized Gaussian measure on C2 -- 11 The Siegel domain case -- Bibliography -- Index.  aThis book is about function spaces aspects of polyanalytic functions, a topic that has gained a lot of attention in the past decades. This book fills a gap in literature and is written by a leading researcher in the field. Rather than studying polyanalytic functions from a complex analysis point of view, it considers the (Lie)-algebraic part of the theory. Several generalizations are offered. The presented theory has many applications, including to quantum physics. An extensive introduction to the topic is provided, making the book accessible to specialists and newcomers alike. 0aFunctions of complex variables.972222 0aOperator theory.14aSeveral Complex Variables and Analytic Spaces.97222524aOperator Theory.24aFunctions of a Complex Variable.9722242 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303176180508iPrinted edition:z978303176182908iPrinted edition:z9783031761836 0aOperator Theory: Advances and Applications,x2296-4878 ;v30597461740uhttps://doi.org/10.1007/978-3-031-76181-2  aZDB-2-SMA  aZDB-2-SXMS  c66232d66232