Titlebook: Distributions, Partial Differential Equations, and Harmonic Analysis; Dorina Mitrea Textbook 2018Latest edition Springer Nature Switzerlan

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The Heat Operator and Related Versions,This chapter has a twofold aim: determine all fundamental solutions that are tempered distributions for the heat operator and related versions (including the Schrödinger operator), then use this as a tool in obtaining the solution of the generalized Cauchy problem for the heat operator.

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The Wave Operator,Here all fundamental solutions that are tempered distributions for the wave operator are determined and then used as a tool in the solution of the generalized Cauchy problem for this operator.

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https://doi.org/10.1007/978-981-16-0819-3features, such as the concept of support, multiplication with a smooth function, distributional derivatives, tensor product, and a partially defined convolution product. Here the nature of distributions with higher order gradients continuous or bounded is also discussed.

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https://doi.org/10.1007/978-3-662-10451-4ns are introduced and studied, including homogeneous and principal value distributions. Significant applications to harmonic analysis and partial differential equations are singled out. For example, a general, higher dimensional jump-formula is deduced in this chapter for a certain class of tempered

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Theory of Quantum Transport at Nanoscaleer. While the natural starting point is the Laplacian, this study encompasses a variety of related operators, such as the bi-Laplacian, the poly-harmonic operator, the Helmholtz operator and its iterations, the Cauchy–Riemann operator, the Dirac operator, the perturbed Dirac operator and its iterati