New convolutions and their applicability to integral equations of Wiener‐Hopf plus Hankel type
Copyright policy )New convolutions and their applicability to integral equations of Wiener‐Hopf plus Hankel type
Algebraic sums of Wiener-Hopf and Hankel operators have received attention in the last years, cf. [\textit{L. P. Castro} et al., Math. Nachr. 269--270, 73--85 (2004; Zbl 1082.47024); \textit{N. Karapetiants} and \textit{S. Samko}, Equations with involutive operators. Boston, MA: Birkhäuser (2001; Zbl 0990.47011)], relevant motivations being the applications to wave diffraction phenomena. In the present paper the authors introduce some mathematical tools suitable for the study of the corresponding equations. Namely, convolutions exhibiting factorization properties are considered, and precise solvability properties are deduced for the equations. An explicit formula for the solution is presented and a Shannon sampling formula is also obtained in this context.
- UNIVERSIDADE DE AVEIRO Portugal
- Vietnam National University, Hanoi Viet Nam
- University of Aveiro (UAVR) Portugal
- Vietnam National University Viet Nam
- University of Aveiro Portugal
Integral operators, Convolution, factorization for one variable harmonic analysis, Convolution, Convolution as an integral transform, integral equation, factorization, Hankel operator, Other transforms and operators of Fourier type, convolution, Wiener-Hopf operator, Factorization, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), Fourier integral operator, Integral equation
Integral operators, Convolution, factorization for one variable harmonic analysis, Convolution, Convolution as an integral transform, integral equation, factorization, Hankel operator, Other transforms and operators of Fourier type, convolution, Wiener-Hopf operator, Factorization, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), Fourier integral operator, Integral equation
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!