On Factorization of Certain Entire-Functions

Certain Hilbert Spaces of Entire Functions

1. Introduction. The research reported on in the present note was motivated by the following Proposition (F), due to Ernest Fischer ([5], see also [4] for an earlier version; actually Fischer proved a more general result, but the special case suffices as a point of departure for our discussion) : (F) Let P denote a homogeneous polynomial in si, • • • , z k with complex coefficients. Then every ...

On the Arithmetical Properties of Certain Entire Characteristic Functions

Muckenhoupt Hamiltonians, triangular factorization, and Krein orthogonal entire functions

According to classical results by M. G. Krein and L. de Branges, for every positive measure μ on the real line R such that ∫ R dμ(t) 1+t2 <∞ there exists a Hamiltonian H such that μ is the spectral measure for the corresponding canonical Hamiltonian system JX ′ = zHX. In the case where μ is an even measure from Steklov class on R, we show that the Hamiltonian H normalized by detH = 1 belongs to...

Almost periodic factorization of certain block triangular matrix functions

Let G(x) = [ eIm 0 c−1e−iνx + c0 + c1e e−iλxIm ] , where cj ∈ Cm×m, α, ν > 0 and α+ ν = λ. For rational α/ν such matrices G are periodic, and their Wiener-Hopf factorization with respect to the real line R always exists and can be constructed explicitly. For irrational α/ν, a certain modification (called an almost periodic factorization) can be considered instead. The case of invertible c0 and ...

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...