Distributions and Generalized Functions
Schwartz distributions, tempered distributions, and Sobolev spaces.
Distributions and Generalized Functions. Schwartz distributions, tempered distributions, and Sobolev spaces.
Foundations and canonical references
The standard treatments of distributions and generalized functions approach the subject from complementary angles. Hormander, The Analysis of Linear Partial Differential Operators I (2003) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Zemanian, Distribution Theory and Transform Analysis (1987) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.
Open methodological questions for distributions and generalized functions include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2003The Analysis of Linear Partial Differential Operators Ihormander-2003
- textbook · supporting · 1987Distribution Theory and Transform Analysiszemanian-1987
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