Tensors and Riemannian Geometry by Nail H. Ibragimov

Author:Nail H. Ibragimov
Language: eng
Format: epub, pdf
Publisher: Walter de Gruyter
Published: 2015-06-15T00:00:00+00:00

Substituting here the Fourier transform ĥ(ξ, λ, u) of h(ξ, y, z) we have:

The inverse Fourier transform of the function (7.1.9) provides the following solution to the particular Cauchy problem (7.1.3):

Here

where and Q(λ, μ) is the quadratic form

with the coefficients

7.1.3Simplification of the solution

Let us rewrite the integral I in a more convenient form. The condition

guarantees that the quadratic form

having the discriminant –Δ(σ) is positive definite. Hence, the quadratic form (7.1.11) is also positive definite since it has the form

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