Convolution powers of complex functions on Z

Convolution powers of complex functions on Z

Repeated convolution of a probability measure on Z leads to the central limit theorem and other limit theorems. This paper investigates what kinds of results remain without positivity. It reviews theorems due to Schoenberg, Greville, and Thomée which are motivated by applications to data smoothing (Schoenberg and Greville) and finite difference schemes (Thomée). Using Fourier transform argument...

study of hash functions based on chaotic maps

توابع درهم نقش بسیار مهم در سیستم های رمزنگاری و پروتکل های امنیتی دارند. در سیستم های رمزنگاری برای دستیابی به احراز درستی و اصالت داده دو روش مورد استفاده قرار می گیرند که عبارتند از توابع رمزنگاری کلیددار و توابع درهم ساز. توابع درهم ساز، توابعی هستند که هر متن با طول دلخواه را به دنباله ای با طول ثابت تبدیل می کنند. از جمله پرکاربردترین و معروف ترین توابع درهم می توان توابع درهم ساز md4, md...

The convolution inequality for entropy powers

On the binomial convolution of arithmetical functions

Let n = ∏ p p νp(n) denote the canonical factorization of n ∈ N. The binomial convolution of arithmetical functions f and g is defined as (f ◦g)(n) = ∑ d|n (∏ p (νp(n) νp(d) )) f(d)g(n/d), where ( a b ) is the binomial coefficient. We provide properties of the binomial convolution. We study the Calgebra (A,+, ◦,C), characterizations of completely multiplicative functions, Selberg multiplicative...

On a Convolution Conjecture of Bounded Functions

We consider the convolution P (A,B) ? P (C,D) of the classes of analytic functions subordinated to the homographies 1+Az 1−Bz and 1+Cz 1−Dz respectively, where A,B, C, D are some complex numbers. In 1988 J. Stankiewicz and Z. Stankiewicz [11] showed that for certain A,B, C, D there exist X, Y such that P (A,B) ? P (C,D) ⊂ P (X, Y ). In this paper we verify the conjecture that P (X, Y ) ⊂ (A,B) ...