On properties of the generalized Davenport Expansion
Alexander E. Patkowski
TL;DR
This paper investigates the continuity properties of a newly discovered generalized Davenport Fourier expansion, analyzing how coefficient conditions affect these properties and relating the expansion to Appell sequences for broader mathematical context.
Contribution
It introduces a generalized Davenport Fourier expansion, explores its continuity under specific coefficient conditions, and connects it to the theory of Appell sequences.
Findings
Continuity depends on specific coefficient conditions.
The expansion can be contextualized within Appell sequences.
Provides theoretical insights into the properties of the generalized expansion.
Abstract
We study the continuity properties of a generalized Davenport Fourier expansion we recently discovered, by imposing conditions on the coefficients. We also put our expansion into perspective from the position of Appell sequences.
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Advanced Banach Space Theory · Stochastic processes and financial applications