Titlebook: Generalized Functions Theory and Technique; Theory and Technique Ram P. Kanwal Book 19982nd edition Birkhäuser Boston 1998 Boundary value p

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The Schwartz-Sobolev Theory of Distributions,tance ., of . from the origin, is . = |.| = (. + . + ... + .).. Let . be an .-tuple of nonnegative integers, . = (., .,..., .), the so-called . of order .; then we define . and . where . = ∂/∂., . = 1, 2,..., .. For the one-dimensional case . reduces to .. Furthermore, if any component of . is zero

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Direct Products and Convolutions of Distributions,spectively. Then a point in the Cartesian product . = . × . is (.) = (.,..., ., .,..., .). Furthermore, let us denote by ., ., and .the spaces of test functions with compact support in ., ., and ., respectively. When . (.) and .(.) are locally integrable functions in the spaces . and ., then the fun

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The Laplace Transform,is variable in this chapter. Let .(.) be a complex-valued function of the real variable . such that .(.). is abolutely integrable over 0 < . < ∞, where . is a real number. Then the Laplace transform of .(.), . ≥ 0, is defined as . where . = . + .. The Laplace transform defined by (1) has the followi

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