Titlebook: Distributions, Partial Differential Equations, and Harmonic Analysis; Dorina Mitrea Textbook 20131st edition Springer Science+Business Med

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More on Fundamental Solutions for Systems,nstant coefficient second order systems in the upper-half space, and the relevance of these operators vis-a-vis to the solvability of boundary value problems for such systems in this setting, are discussed.

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Weak Derivatives,ced as a mean of extending the notion of solution to a more general setting, where the functions involved may lack standard pointwise differentiability properties. Here two classes of test functions are also defined and discussed.

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–FER

The Space of Tempered Distributions,s 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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engagement

The Laplacian and Related Operators,er. 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 Cauchy-Riemann operator, the Dirac operator, as well as general second order constant coefficient strongly elliptic operators. Havin

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More on Fundamental Solutions for Systems,cases of the approach developed, fundamental solutions that are tempered distributions for the Lamé and Stokes operators are derived. The fact that integral representation formulas and interior estimates hold for null-solutions of homogeneous systems with non-vanishing full symbol is also proved. As

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Arboreal

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