Hančl, Jaroslav A note to the Fourier method of solving partial second-order differential equations. (English) Zbl 0703.35039 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 91, Math. 27, 299-306 (1988). Consider the linear differential operator \[ Lu(x,y)=a_ 1(x)u_{xx}(x,y)+a_ 2(x)u_ x(x,y)+a_ 3(x)u(x,y)- \]\[ -b_ 1(y)u_{yy}(x,y)-b_ 2(y)u_ y(x,y)-b_ 3(y)u(x,y) \] for (x,y)\(\in I\times J\) (two bounded or unbounded intervals). The author solves the equation \(Lu(x,y)=0\) by means of the classical Kummer transform. Reviewer: J.Appell Cited in 1 ReviewCited in 1 Document MSC: 35G05 Linear higher-order PDEs 35A22 Transform methods (e.g., integral transforms) applied to PDEs Keywords:Kummer transform × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] Bochner S., Chandrasekaran K. C.: Fourier Transforms. Princeton, 1949. [2] Kufner A., Kadlec J.: Fourier series. Praha, Academia, 1969. · Zbl 0215.17901 [3] Laitoch M.: To a problem of ortogonal systems with weight. Acta. Univ. Olom. 3 (1960), 11-28) [4] Widder D. W.: The Laplace Transform. Princeton, 1946. · Zbl 0060.24801 · doi:10.2307/2305640 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.