The Bedrosian identity for generalized functions
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6964
Abstract: The object of this paper is to develop sufficient conditions for the Bedrosian identity of functions in space Lp(ℝn) . We generalize the result of Zhang for L2(ℝn) functions (2014). Meanwhile, the Bedrosian identity for… read more here.
Keywords: identity generalized; generalized functions; bedrosian identity; identity ... See more keywords
Rigorous implementation of the Galerkin method for stepped structures needs generalized functions
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Sound and Vibration"
DOI: 10.1016/j.jsv.2020.115708
Abstract: Abstract In this paper we study free vibrations of stepped structures, specifically for longitudinal vibrations of bars and flexural vibrations of rectangular plates, providing two versions of the Galerkin method. Specifically, we first apply the… read more here.
Keywords: stepped structures; method; galerkin method; rigorous implementation ... See more keywords
A Convenient Notion of Compact Set for Generalized Functions
Sign Up to like & getrecommendations! Published in 2017 at "Proceedings of the Edinburgh Mathematical Society"
DOI: 10.1017/s0013091516000559
Abstract: We introduce the notion of functionally compact sets into the theory of nonlinear generalized functions in the sense of Colombeau. The motivation behind our construction is to transfer, as far as possible, properties enjoyed by… read more here.
Keywords: convenient notion; notion compact; compact set; notion ... See more keywords
Non-linear expectations in spaces of Colombeau generalized functions
Sign Up to like & getrecommendations! Published in 2019 at "Stochastic Analysis and Applications"
DOI: 10.1080/07362994.2019.1585265
Abstract: Abstract We introduce the notion of a non-linear expectation in spaces of Colombeau generalized functions and provide its characterization in terms of the upper expectation over a set of probability measures. We then study a… read more here.
Keywords: colombeau generalized; expectations spaces; non linear; linear expectations ... See more keywords
High-Frequency Radar Cross Section of the Ocean Surface With Arbitrary Roughness Scales: A Generalized Functions Approach
Sign Up to like & getrecommendations! Published in 2021 at "IEEE Transactions on Antennas and Propagation"
DOI: 10.1109/tap.2020.3026330
Abstract: A correction term for electromagnetic scattering from the ocean surface with large roughness scales in the HF band is proposed. A generalized functions’ method has been employed to obtain the operator equation of the electric… read more here.
Keywords: generalized functions; ocean surface; cross section; roughness scales ... See more keywords
The Fractional Hilbert Transform of Generalized Functions
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DOI: 10.3390/sym14102096
Abstract: The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its widespread application in optics, engineering, and signal processing. In the present work, we expand the… read more here.
Keywords: fractional hilbert; transform; transform generalized; hilbert transform ... See more keywords