منابع مشابه
Sampling and Generalized Almost Periodic Extension of Functions
This brief explores the connections between nonuniform sampling of a certain function and the almost periodic extension of its Fourier transform. It is shown that the Fourier transform of a band-limited function can be extended (as a weighted sum of translates) as a Stepanoff almost periodic function to the whole frequency axis. This result leads to a generalized nonuniform sampling theorem whi...
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Almost periodic functions form a natural example of a non-separable normed space. As such, it has been a challenge for constructive mathematicians to find a natural treatment of them. Here we present a simple proof of Bohr’s fundamental theorem for almost periodic functions which we then generalize to almost periodic functions on general topological groups.
متن کاملOn Hartman Almost Periodic Functions
In this note we consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in R or Z. We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally co...
متن کاملComputing with almost periodic functions.
This paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis around the emerging theory of quasicrystals and diffraction in the setting on local hulls and dynamical systems. Numerically computed approximations arising in this way are built out of the Fourier module of the quasi...
متن کاملComposition Theorems of Stepanov Almost Periodic Functions and Stepanov-Like Pseudo-Almost Periodic Functions
We establish a composition theorem of Stepanov almost periodic functions, and, with its help, a composition theorem of Stepanov-like pseudo almost periodic functions is obtained. In addition, we apply our composition theorem to study the existence and uniqueness of pseudo-almost periodic solutions to a class of abstract semilinear evolution equation in a Banach space. Our results complement a r...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1970
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-22-1-121-133