Let denote the class of analytic functions f = {f 1, f 2, ⦠, f s } on the unit disk U satisfying where and is the extended Ruscheweyh derivative defined by and h is convex univalent in U with h(0) = 1. Also let F = {F 1, F 2, ⦠, F s }, ...
This paper is a review of some of our relevant work on bi-analytic functions and their applications in elasticity. The main basis lies in a mechanical interpretation of bi-analytical functions. First we provide a brief introduction of (λ,k) bi-analytical functions and the relation between the...
Theorem1follows from Theorem2.7in Sect.2.1.2. Thus, all analytic functions in a finitely generated space\(S_\Phi \)are exponential polynomials of the form (1) with coefficients being arbitrary analytic 1-periodic functions\(\omega _{j,k}\). We would like to emphasize thatHis only a subsp...
Of course the functions from map the unit disc onto convex domains. We say that the functionf∈His subordinate to the functiong∈Hin the unit disc Δ (writtenf≺g) if and only if there exists an analytic functionw∈Hsuch thatw(0)=0,|w(z)|<1andf(z)=g(w(z))forz∈Δ. Therefo...
Complex Numbers and Functions Nakhlé H. Asmar, Loukas Grafakos Pages 1-94 Analytic Functions Nakhlé H. Asmar, Loukas Grafakos Pages 95-138 Complex Integration Nakhlé H. Asmar, Loukas Grafakos Pages 139-226 Series of Analytic Functions and Singularities Nakhlé H. Asmar, Loukas Gr...
Let A be the class of analytic functions in the open unit disk U. Given 0 ≤λ < 1, let Ωλ be the operator defined on A by (ωλf)(z)=Γ(2-λ)z λD λ zf(z), where D λ z f is the fractional derivative of f of order λ. A function f in A is said to be in ...
classification of data, which produces different functional groups (or clusters) for gaining more sophisticated knowledge of different pathways and/or functions for large scale data; (3) functional linear models used for testing the effects on outcomes in functional form; and (4) forecasting via...
Mathematically, if a two-dimensional (2D) analytic function is known exactly in an arbitrarily small spectral region, then the entire function can be determined uniquely by means of analytic continuation33. The diffraction limit of an optical imaging system can be overcome to some extent at the ...
Of course the functions from map the unit disc onto convex domains. We say that the function f∈H is subordinate to the function g∈H in the unit disc Δ (written f≺g) if and only if there exists an analytic function w∈H such that w(0)=0, |w(z)|<1 and f(z)=g(w(z)...
of automorphicL-function in the analytic conductor aspect. The new ideas of the proofs include the use of analytic newvectors to construct an approximate projector on the automorphic spectrum with bounded conductors and a soft local (both at finite and infinite places) analysis of the geometric ...