Journal ArticleDOI
Spectral factorization in the disk algebra
Holger Boche,Volker Pohl +1 more
- Vol. 50, Iss: 6, pp 383-387
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TLDR
In this article, it was shown that even if the given function f on the boundary is continuous, the corresponding outer function is generally not continuous on the closure of the unit disk, and that any subset E∈ [-π,π) of Lebesgue measure zero is a valid divergence set for outer functions of some continuous functions f.Abstract:
Every strictly positive function f, given on the unit circle of the complex plane, defines an outer function. This article investigates the behavior of these outer functions on the boundary of the unit disk. It is shown that even if the given function f on the boundary is continuous, the corresponding outer function is generally not continuous on the closure of the unit disk. Moreover, any subset E∈ [-π ,π) of Lebesgue measure zero is a valid divergence set for outer functions of some continuous functions f. These results are applied to study the solutions of non-linear boundary-value problems and the factorization of spectral density functions.read more
Citations
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Proceedings ArticleDOI
Continuity of the Outer Factorization and Mapping Properties with Applications
Holger Boche,Volker Pohl +1 more
TL;DR: In this article, the authors investigated the smoothness properties of the Poosson integral and conjugate Poisson integral on the closure of the unit disk and gave sufficient and necessary conditions on the majorants of the data such that these integrals as well as the Hilbert- and Cauchy transform have always the same modulus of continuity as the data, provided that the data have no zeros on the unit circle.
Journal ArticleDOI
Behaviour of the spectral factorization for continuous spectral densities
Holger Boche,Volker Pohl +1 more
TL;DR: It is shown in this paper that every continuous spectrum is a discontinuity point of the spectral factorization, and that this error grows proportional with the logarithm of the number N of Fourier coefficients which are taken into account.
Journal ArticleDOI
Characterization of holomorphic functions in terms of their moduli
Holger Boche,Volker Pohl +1 more
TL;DR: Boche and Pohl as discussed by the authors showed that if the modulus of continuity of a function is a weak regular majorant, the continuity of the Modulus always implies the continuoustime of the function itself.
Journal ArticleDOI
Spectral Factorization for Polynomial Spectral Densities—Impact of Dimension
Holger Boche,Volker Pohl +1 more
TL;DR: The correspondence derives a lower bound on the continuity constant of the spectral factorization mapping which shows that the error in the spectral factors grows at least proportional with the logarithm of the degree N of the given spectrum.
Proceedings ArticleDOI
Characterization of the behavior of outer functions with applications to spectral factorization and system design
Holger Boche,Volker Pohl +1 more
TL;DR: This paper investigates the continuity behavior of the outer factorization mapping and it gives a characterization of all outer functions which belong to the same smoothness class as the corresponding data.
References
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Book
Bounded Analytic Functions
TL;DR: In this article, the Corona construction was used to construct Douglas algebra and interpolating sequences and Maximal Ideals were used to solve a set of problems in the Corona Construction.
Book
Statistical Digital Signal Processing and Modeling
TL;DR: The main thrust is to provide students with a solid understanding of a number of important and related advanced topics in digital signal processing such as Wiener filters, power spectrum estimation, signal modeling and adaptive filtering.
Book
Extrapolation, Interpolation, and Smoothing of Stationary Time Series: With Engineering Applications
TL;DR: Extrapolation interpolation and smoothing of stationary, stationary tones interference cancellation using adaptive and stationary time series financial definition of stationary.
Journal ArticleDOI
On bounded analytic functions
TL;DR: In this article, the authors give an alternative derivation of results on bounded analytic functions recently obtained by Ahlfors [1] and Garabedian [2] and show that the main idea to be used is more in the nature of a lucky guess than of a method.