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

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生意行為

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 Schr?dinger operator), then use this as a tool in obtaining the solution of the generalized Cauchy problem for the heat operator.

prosperity

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.

Transfusion

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浮雕

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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