Asymptotics of the scattered Debye potentials via a generalized convolution. (English) Zbl 1347.42012
Summary: In this paper, we express the scattered Debye potentials via a new generalized convolution related to the Kontorovich-Lebedev integral. The uniform asymptotics of the scattered Debye potentials under very mild conditions on the spectral functions are obtained, and an inverse problem of finding spectral functions from given Debye potentials is considered.
MSC:
| 42A85 | Convolution, factorization for one variable harmonic analysis |
| 44A35 | Convolution as an integral transform |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
References:
| [1] | DOI: 10.1093/imamat/69.3.285 · Zbl 1115.78005 · doi:10.1093/imamat/69.3.285 |
| [2] | DOI: 10.1093/imamat/hxq030 · Zbl 1214.35067 · doi:10.1093/imamat/hxq030 |
| [3] | DOI: 10.1142/9789812831064 · doi:10.1142/9789812831064 |
| [4] | DOI: 10.1007/s00025-009-0393-x · Zbl 1180.44004 · doi:10.1007/s00025-009-0393-x |
| [5] | DOI: 10.1080/10652460903101919 · Zbl 1191.44002 · doi:10.1080/10652460903101919 |
| [6] | Prudnikov AP, Integrals and series: special functions (1986) |
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