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Results tagged with differential-operators
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user 750
Elliptic, parabolic and hyperbolic operators. Laplace, Laplace-Beltrami, Schrödinger, Dirac. Exterior derivative and Lie derivative operators.
5
votes
Idempotents in Rings of Differential Operators
Here's a cute partial result, classifying idempotents of order 1.
Let $\delta$ be an idempotent differential operator of order 1. Then there is a unique decomposition $R\simeq A\oplus M$, with $A$ a …
- 13k
26
votes
1
answer
990
views
Idempotents in Rings of Differential Operators
Differential Operators on General Commutative Rings
Let k be an algebraically closed field of characteristic zero, and let R be a commutative k-algebra. Then a (Grothendieck) differential operator on …
- 13k
12
votes
1
answer
640
views
Does the image of a differential operator always contain an ideal?
Let $\delta$ denote a non-zero complex algebraic differential operator in a single variable x. That is, it can be written as a sum
$$ \delta = \sum_i f_i\partial_x^i$$
where there $f_i$ are complex p …
- 13k