Bohr proved that a uniformly almost periodic function f has a bounded spectrum if and only if it extends to an entire function F of exponential type τ(F ) < ∞. If f ≥ 0 then a result of Krein implies that f admits a factorization f = |s|2 where s extends to an entire function S of exponential type τ(S) = τ(F )/2 having no zeros in the open upper half plane. The spectral factor s is unique up to a multiplicative factor having modulus 1. Krein and Levin constructed f such that s is not uniformly… Expand

Since Helmer's 1940 paper [9] laid the foundations for the study of the ideal theory of the ring A(C) of entire functions!, many interesting results have been obtained for the rings A(X) of analytic… Expand

These lecture notes present an extensive review of the factorization theory of matrix functions relative to a curve with emphasis on the developments of the last 20–25 years. The classes of functions… Expand

II. Differentiation II.2. Examples of differentiation. The case of one variable (n = 1). II.2.3. Pseudofunctions. Hadamard finite part. We calculate the derivative of a function f(x) which is equal… Expand

It is proved that if positive definite matrix functions (i.e. matrix spectral densities) Sn, n=1,2,… , are convergent in the L1-norm, $\|S_{n}-S\|_{L_{1}}\to 0$, and $\int_{0}^{2\pi}\log… Expand