Matches in SemOpenAlex for { <https://semopenalex.org/work/W3176294723> ?p ?o ?g. }
- W3176294723 endingPage "75" @default.
- W3176294723 startingPage "37" @default.
- W3176294723 abstract "This is a short introduction to the theory of holomorphic functions in finitely and infinitely many variables. We begin with functions in finitely many variables, giving the definition of holomorphic function. Every such function has a monomial series expansion, where the coefficients are given by a Cauchy integral formula. Then we move to infinitely many variables, considering functions defined on B_{c0}, the open unit ball of the space of null sequences. Holomorphic functions are defined by means of Frechet differentiability. We have versions of Weierstrass and Montel theorems in this setting. Every holomorphic function on B_{c0} defines a family of coefficients through a Cauchy integral formula and a (formal) monomial series expansion. Every bounded analytic (represented by a convergent power series) function is holomorphic. Hilbert’s criterion, that gives conditions on a family of scalars so that it is attached to a bounded holomorphic function on B_{c0}. Homogeneous polynomials are those entire functions having non-zero coefficients only for multi-indices of a given order. We show how these are related to multilinear forms on c0 through the polarization formulas." @default.
- W3176294723 created "2021-07-05" @default.
- W3176294723 creator A5002208194 @default.
- W3176294723 creator A5027091446 @default.
- W3176294723 creator A5035736049 @default.
- W3176294723 creator A5086529737 @default.
- W3176294723 date "2019-08-08" @default.
- W3176294723 modified "2023-09-23" @default.
- W3176294723 title "Holomorphic Functions on Polydiscs" @default.
- W3176294723 cites W1008327673 @default.
- W3176294723 cites W104186297 @default.
- W3176294723 cites W1173888621 @default.
- W3176294723 cites W1422028892 @default.
- W3176294723 cites W142734103 @default.
- W3176294723 cites W1486737258 @default.
- W3176294723 cites W1502986712 @default.
- W3176294723 cites W1506153731 @default.
- W3176294723 cites W1535215800 @default.
- W3176294723 cites W153641107 @default.
- W3176294723 cites W1546372806 @default.
- W3176294723 cites W1547644141 @default.
- W3176294723 cites W1570957364 @default.
- W3176294723 cites W1575826768 @default.
- W3176294723 cites W1575834508 @default.
- W3176294723 cites W1585417868 @default.
- W3176294723 cites W1590432342 @default.
- W3176294723 cites W1593621363 @default.
- W3176294723 cites W1604321310 @default.
- W3176294723 cites W1639241133 @default.
- W3176294723 cites W1661802750 @default.
- W3176294723 cites W1677627604 @default.
- W3176294723 cites W187421296 @default.
- W3176294723 cites W1878875441 @default.
- W3176294723 cites W1966727818 @default.
- W3176294723 cites W1969714776 @default.
- W3176294723 cites W1970240397 @default.
- W3176294723 cites W1975540652 @default.
- W3176294723 cites W1976601523 @default.
- W3176294723 cites W1976921741 @default.
- W3176294723 cites W1980267449 @default.
- W3176294723 cites W1982157240 @default.
- W3176294723 cites W1985804647 @default.
- W3176294723 cites W1992798754 @default.
- W3176294723 cites W1996618611 @default.
- W3176294723 cites W1997281570 @default.
- W3176294723 cites W1999657274 @default.
- W3176294723 cites W2000138118 @default.
- W3176294723 cites W2002687757 @default.
- W3176294723 cites W2007399766 @default.
- W3176294723 cites W2007927352 @default.
- W3176294723 cites W2012219146 @default.
- W3176294723 cites W2013665084 @default.
- W3176294723 cites W2014541585 @default.
- W3176294723 cites W2015100233 @default.
- W3176294723 cites W2016080679 @default.
- W3176294723 cites W2017399891 @default.
- W3176294723 cites W2018987216 @default.
- W3176294723 cites W2022493922 @default.
- W3176294723 cites W2029839905 @default.
- W3176294723 cites W2030604695 @default.
- W3176294723 cites W2031385330 @default.
- W3176294723 cites W2034600980 @default.
- W3176294723 cites W2039073800 @default.
- W3176294723 cites W2040745222 @default.
- W3176294723 cites W2044705601 @default.
- W3176294723 cites W2045264417 @default.
- W3176294723 cites W2049385891 @default.
- W3176294723 cites W2051222651 @default.
- W3176294723 cites W2052381931 @default.
- W3176294723 cites W2057944389 @default.
- W3176294723 cites W2063752210 @default.
- W3176294723 cites W2064116667 @default.
- W3176294723 cites W2064830800 @default.
- W3176294723 cites W2065069526 @default.
- W3176294723 cites W2065481426 @default.
- W3176294723 cites W2067282767 @default.
- W3176294723 cites W2067954732 @default.
- W3176294723 cites W2068999809 @default.
- W3176294723 cites W2069754508 @default.
- W3176294723 cites W2070530652 @default.
- W3176294723 cites W2071930777 @default.
- W3176294723 cites W2072062508 @default.
- W3176294723 cites W2072417204 @default.
- W3176294723 cites W2072792056 @default.
- W3176294723 cites W2073093847 @default.
- W3176294723 cites W2078223006 @default.
- W3176294723 cites W2078904307 @default.
- W3176294723 cites W2080171332 @default.
- W3176294723 cites W2081054398 @default.
- W3176294723 cites W2081183814 @default.
- W3176294723 cites W2081531738 @default.
- W3176294723 cites W2083561748 @default.
- W3176294723 cites W2087459407 @default.
- W3176294723 cites W2088365357 @default.
- W3176294723 cites W2088772065 @default.
- W3176294723 cites W2089844308 @default.
- W3176294723 cites W209159601 @default.
- W3176294723 cites W2091773229 @default.