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Results tagged with generalized-functions
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user 11260
4
votes
Colombeau generalized functions
This recent textbook might be helpful:
Geometric Theory of Generalized Functions with Applications to General Relativity, M. Grosser, M. Kunzinger, M. Oberguggenberger, and R. Steinbauer (2013).
…
- 188k
10
votes
Make mathematical sense of the Dirac well Potential Equation
If you wish to avoid delta functions, you could just Fourier transform,
$f(k)=\int_{-\infty}^\infty e^{ikx}y(x)dx$. The differential equation then transforms into
$$(k^2+\lambda^2) f(k)=y(0)$$
Divid …
- 188k
6
votes
Generalized functions in infinite dimensions
The study of an "infinite-dimensional delta function" has been motivated to a large extent by applications in quantum field theory. Here is some relevant literature:
Tempered distributions in infinit …
- 188k
10
votes
Anti-delta function?
To elaborate on the comment, I would suggest to take $F(x)=x^{-2}\delta(1/x)$. Let me check for the representation
$\delta_{\epsilon}(x)=(2\pi\epsilon)^{-1/2}e^{-x^2/2\epsilon}$,
and $F_\epsilon(x)=x^ …
- 188k
3
votes
Accepted
English translation of Schwartz's papers on vector-valued distributions
These papers have not been translated, as far as I know, however there exist lecture notes in english of courses by Schwarz on this topic:
• Introduction to the Theory of Distributions
• Lectures on …
- 188k