• Corpus ID: 233296391

Note on Spectral Factorization Results of Krein and Levin

@inproceedings{Lawton2021NoteOS,
  title={Note on Spectral Factorization Results of Krein and Levin},
  author={Wayne M. Lawton},
  year={2021}
}
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… 

References

SHOWING 1-10 OF 32 REFERENCES

OF ENTIRE FUNCTIONS

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

An Overview of Matrix Factorization Theory and Operator Applications

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

Théorie des distributions

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

Hardy Classes And Operator Theory

On Approximate Spectral Factorization of Matrix Functions

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

Zur Theorie der fastperiodischen Funktionen

Wir betrachten die Menge aller endlichen Summen $$\begin{array}{*{20}c} {s\left( \chi \right) = \sum\limits_{n = 1}^N {a_n e^{i\lambda _n x} } ,} & {\quad - \infty < \chi < \infty ,} \\

The Zeros of Certain Integral Functions

Levin

  • Distribution of Roots of Entire Functions, Translations of Mathematical Monographs, Volume 5, Revised Edition, American Mathematical Society
  • 1964