## A note to the Fourier method of solving partial second-order differential equations.(English)Zbl 0703.35039

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

### MSC:

 35G05 Linear higher-order PDEs 35A22 Transform methods (e.g., integral transforms) applied to PDEs

Kummer transform
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### 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
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