Exponentials form a basis of discrete holomorphic functions
نویسنده
چکیده
We show that discrete exponentials form a basis of discrete holomorphic functions. On a convex, the discrete polynomials form a basis as well.
منابع مشابه
The Product of Exponentials in the Definition of Canonical Kernel Function
The canonical kernel function of a bounded symmetric domain D in its Harish-Chandra realization has been introduced by I. Satake in [8, 9, 10, 11] and since then it has found several applications. Some of them would include reproducing kernels for Hilbert spaces of holomorphic functions on D associated with the holomorphic discrete series representations, the commutator of certain elements in t...
متن کاملA special subspace of weighted spaces of holomorphic functions on the upper half plane
In this paper, we intend to define and study concepts of weight and weighted spaces of holomorphic (analytic) functions on the upper half plane. We study two special classes of these spaces of holomorphic functions on the upper half plane. Firstly, we prove these spaces of holomorphic functions on the upper half plane endowed with weighted norm supremum are Banach spaces. Then, we investigate t...
متن کاملA remark on boundedness of composition operators between weighted spaces of holomorphic functions on the upper half-plane
In this paper, we obtain a sucient condition for boundedness of composition operators betweenweighted spaces of holomorphic functions on the upper half-plane whenever our weights are standardanalytic weights, but they don't necessarily satisfy any growth condition.
متن کاملUnivalent holomorphic functions with fixed finitely many coefficients involving Salagean operator
By using generalized Salagean differential operator a newclass of univalent holomorphic functions with fixed finitely manycoefficients is defined. Coefficient estimates, extreme points,arithmetic mean, and weighted mean properties are investigated.
متن کاملTwo Equivalent Presentations for the Norm of Weighted Spaces of Holomorphic Functions on the Upper Half-plane
Introduction In this paper, we intend to show that without any certain growth condition on the weight function, we always able to present a weighted sup-norm on the upper half plane in terms of weighted sup-norm on the unit disc and supremum of holomorphic functions on the certain lines in the upper half plane. Material and methods We use a certain transform between the unit dick and the uppe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008