Generalized Functions: Theory and Applications

By R. Kanwal. 2004

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A Note on the Triple Laplace Transform and Its Applications to Some Kind of Third-Order Differential Equation (2013, unknown): “0 exp [−px] exp [−sy] × exp [−kt] f (x, y, t) dx dy dt (14) is convergent at the point (p, s, k); for the readers who are interested, they can see the proof in [11, 12].”
Measuring regional inequality: to weight or not to weight? (2018, background): “It is defined as δ(x) = 0 everywhere except at zero and δ(0) =∞ so that 1 −1 d(x)dx = 1 (e.g., Kanwal, 2004).”
Integrated layout design of multi-component systems using XFEM and analytical sensitivity analysis (2012, background): “The definition of the Heaviside function [37] is:”
Resolution of Policy Uncertainty and Sudden Declines in Volatility (2017, background): “Fourier transform is well-defined for a tempered distribution, see Kanwal (2004).”
A new integral transform and associated distributions (2010, background): “Similarly, if we consider the regular distribution f (t) = H(t) ln(t) [6], then it follows that”