See differential operator on Wiktionary
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"text": "Define P(D) to be the differential operator given by P(D)#x3D;D²#x2B;5D#x2B;6, where D is the differentiation operator. Then P(D)(#x5C;sin(x))#x3D;-#x5C;sin(x)#x2B;5#x5C;cos(x)#x2B;6.",
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"ref": "2000, S. Albeverio, P. Kurasov, Singular Perturbations of Differential Operators, page 328:",
"text": "[…]these conditions appeared in the very first papers on ordinary differential operators.",
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"ref": "2012, Youri Egorov, Bert-Wolfgang Schulze, Pseudo-Differential Operators, Singularities, Applications, page 27:",
"text": "A differential operator P#x5C;left(D#x5C;right) is hypoelliptic if for any domain ⊂ #x5C;mathbb#x7B;R#x7D;ⁿ any solution u of the equation P#x5C;left(D#x5C;right)u#x3D;0 from the class #x5C;mathfrak#x7B;D#x7D;'#x5C;left(#x5C;Omega#x5C;right) is a function from C#x5C;infty(ω) for any open set ω ⊂⊂ #x5C;Omega.\nA complete algebraic description of all hypoelliptic differential operators has been obtained by Hörmander in [H1].",
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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