Integral representation of one class of entire functions
نویسندگان
چکیده
In this paper, we study an integral representation of one class entire functions. Conditions for the existence in terms certain solutions some differential equations are found. We obtain asymptotic estimates functions from considered also give examples class.
منابع مشابه
On the Integral Representations of Generalized Relative Type and Generalized Relative Weak Type of Entire Functions
In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.
متن کاملIntegral Representation of Whittaker Functions
Here W is in the Whittaker model W(π, ψ) of a unitary generic representation π of GL(n, F) and W ′ in W(π ′, ψ) where π ′ is a unitary generic representation of GL(n − 1, F) (see below for unexplained notations). One of the difficulties of the theory is that the representations π and π ′ need not be tempered. Thus one is led to consider holomorphic fiber bundles of representations (πu) and (π ′...
متن کاملGrowth analysis of entire functions of two complex variables
In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.
متن کاملOne-sided approximation by entire functions
Let f : R→ R have an nth derivative of finite variation Vf(n) and a locally absolutely continuous (n− 1)st derivative. Denote by E±(f, δ)p the error of onesided approximation of f (from above and below, respectively) by entire functions of exponential type δ > 0 in Lp(R)–norm. For 1 ≤ p ≤ ∞ we show the estimate E±(f, δ)p ≤ C n π1/pVf(n)δ −n− 1 p , with constants Cn > 0.
متن کاملINTEGRAL REPRESENTATION OF CONTINUOUS FUNCTIONS(x)
It was shown by F. Riesz [5; 350](2) that every subharmonic function u can be represented as the sum of the potential of its mass distribution plus a harmonic function; the potential appears in the form of a Stieltjes integral (Riesz's theorem is stated in (2.2.1)). We prove that the Stieltjes integral may be replaced by a Lebesgue integral if u is continuous, and if the lower generalized Lapla...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Armenian journal of mathematics
سال: 2022
ISSN: ['1829-1163']
DOI: https://doi.org/10.52737/18291163-2022.14.1-1-9