Metric convolution and frames

The fractal convolution of two mappings is a binary operation in some space of functions. In previous papers we extracted the main properties of this association and defined a new type of inner operations in metric spaces, not necessarily linked to fractal theory. This operation has been called metr...

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Bibliographic Details
Published inPeriodica mathematica Hungarica Vol. 88; no. 1; pp. 243 - 265
Main Authors Pasupathi, R., Navascués, M. A., Chand, A. K. B., Mohapatra, R. N.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2024
Springer Nature B.V
Subjects
Convolution
Fractals
Mathematics
Mathematics and Statistics
Metric space
Frames
46B15
Fractal
Metric convolution
30L15
47B02
28A80
Hilbert spaces
37B25
Riesz bases
Dynamical system
Positively stable
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Summary:The fractal convolution of two mappings is a binary operation in some space of functions. In previous papers we extracted the main properties of this association and defined a new type of inner operations in metric spaces, not necessarily linked to fractal theory. This operation has been called metric convolution, though it does not agree with the classical convolution of functions. In this paper we develop a further insight into this association, deducing additional properties. When the metric space framework is substituted by a normed space setting, we address the definition of bases and frames composed of convolution elements, different from those of other articles. We study also the dynamics of two maps linked to the operation.
ISSN:0031-5303
1588-2829
DOI:10.1007/s10998-023-00550-5