Integral transforms connected with differential systems with a singularity.
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Abstract
We consider some integral transforms with the kernels expressed in terms of solutions of the system of differential equations \( y'=(x^{-1}A+B)y, \) where \(A\) and \(B\) are constant \(n\times n\), \(n>2\) , matrices. We study analytical and asymptotical properties of such transforms. We also study the transforms as operators acting in some functional spaces.
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Ignatiev, M. (2019). Integral transforms connected with differential systems with a singularity. Tamkang Journal of Mathematics, 50(3), 253–268. https://doi.org/10.5556/j.tkjm.50.2019.3353
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References
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[2] Levitan, B. M. Expansion in Fourier series and integrals with Bessel functions. (Russian) Uspehi Matem. Nauk (N.S.) 6, (1951). no. 2(42), 102-143.
[3] Yurko V. , On integral transforms connected with differential operators having singularities inside the interval. Integral Transforms and Special Functions, 1997, Vol.5, No. 3–4. Pp. 309– 322.
[4] Yurko V. , Integral transforms connected with higher-order differential operators with a sin- gularity. Integral Transforms and Special Functions, 2002, Vol.13, pp. 497–511.
[5] Ignatyev M., Spectral analysis for differential systems with a singularity. Results in Mathe- matics, 2017, Vol. 71., pp. 1531
[6] Beals R., Deift P. and Tomei C., Direct and inverse scattering on the line, American Mathe- matical Society, Providence, Rhod Island (1988).
[7] Y. Sibuya, Stokes phenomena, Bull. Amer. Math. Soc., 1977, Vol.83, No.5, 1075-1077.
[8] Fedoryuk M. V., Isomonodromy deformations of equations with irregular singularities., (Rus- sian) Mathematics of the USSR-Sbornik 1992,71, No.2. Pp. 463–479.
[9] Sedletskiy A. M. , Classes of analytic Fourier transforms and exponential approximations. (Russian) Moscow, Fizmatlit, 2005. 504 p.