On the polyconvolution with the weight function γ(y)=cosy of Hartley integral transforms H1, H2, H1 and integral equations
DOI:
https://doi.org/10.37863/umzh.v75i4.6971Keywords:
Integral equation, convolution, polyconvolution, Hartley transformsAbstract
UDC 517.5
We construct and investigate new polyconvolution with the weight function γ(y)=cosy of Hartley integral transforms H1, H2, H1 and apply it to solve integral equations and a system of integral equations of polyconvolution type.
References
N. L. R. Achiezer, Lectures on approximation theory, Sci. Publ. House, Moscow (1965).
P. K. Anh, N. M. Tuan, P. D Tuan, The finite Hartley new convolutions and solvability of the integral equations with
Toeplitz plus Hankel kernels, J. Math. Anal. and Appl., 397, № 2, 537–549 (2013). DOI: https://doi.org/10.1016/j.jmaa.2012.07.041
R. N. Bracewell, The Hartley transform, Oxford Univ. Press, Clarendon Press, New York (1986).
F. D. Gakhov, Ya. I. Cerskii, Equations of convolution type, Nauka, Moscow (1978).
B. T. Giang, N. V. Mau, N. M. Tuan, Operational properties of two integral transforms of Fourier type and their convolutions, Integral Equations Operator Theory, 65, № 3, 363–386 (2009). DOI: https://doi.org/10.1007/s00020-009-1722-x
B. T. Giang, N. V. Mau, N. M. Tuan, Convolutions for the Fourier transforms with geometric variables and applications, Math. Nachr., 283, № 12, 1758–1770 (2010). DOI: https://doi.org/10.1002/mana.200710192
V. A. Kakichev, Polyconvolution, TPTU, Taganrog (1997).
V. V. Napalkov, Convolution equations in multidimensional space, Nauka, Moscow (1982).
T. Kailath, Some integral equations with 'nonrational' kernels, IEEE Trans. Inform. Theory, 12, № 4, 442–447 (1966). DOI: https://doi.org/10.1109/TIT.1966.1053925
N. M. Khoa, T. V. Thang, On the polyconvolution of Hartley integral transforms H2 and integral equations, J. Integral Equat. and Appl., 322, 171–180 (2020).
N. M. Khoa, D. X. Luong, On the polyconvolution of Hartley integral transforms H1,H2,H1 and integral equations, Austral. J. Math. Anal. and Appl., 16, № 2, 1–10 (2019). DOI: https://doi.org/10.1216/jie.2020.32.171
N. X. Thao, H. T. V. Anh, On the Hartley–Fourier sine generalized convolution, Math. Methods Appl. Sci., 37, № 5, 2308–2319 (2014). DOI: https://doi.org/10.1002/mma.2980
N. X. Thao, N. M. Khoa, P. T. V. Anh, Polyconvolution and the Toeplitz plus Hankel integral equation, Electron. J. Different. Equat., 2014, № 110, 1–14 (2014).
N. X. Thao, N. M. Khoa, P. T. V. Anh, Integral transforms of Hartley, Fourier cosine and Fourier sine polyconvolution type, Vietnam J. Math. Appl., 12, № 4, 93–104 (2014).
