Abstract
In this chapter the space of distributions is introduced and studied from the perspective of a topological vector space with various other additional features, 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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Mitrea, D. (2013). The Space \(\mathcal{D}^{\prime}(\Omega )\) of Distributions. In: Distributions, Partial Differential Equations, and Harmonic Analysis. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8208-6_2
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DOI: https://doi.org/10.1007/978-1-4614-8208-6_2
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