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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

0 votes
1 answer
479 views

Discrete Sobolev space of $R^n$ valued maps

Can some one tell me the reference or any idea how to take the Discrete Sobolev space work defined for a scalar valued map to the space of maps which are vector valued.Let's say $f:\Omega \rightarro …
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1 vote
2 answers
1k views

Existence of solution of a Non-linear PDE via Fixed point theorem

Hi all I've the following non-linear PDE $-\Delta Y + Y^3 =U$ on $\Omega \subset R^n $, open, bounded, Lipschitz boundary domain $Y=0 , $ on $\partial\Omega$ 1.Let $Y\in H_0^1 $ and as $H_0^1 \hoo …
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0 votes
1 answer
142 views

A special Integral Kernel

Does there exist either one / general class of non-negative definite , symmetric Integral Kernel map satisfying the following properties ?? $f(x)=(Kg)(x)=\int_{\Omega}K(x,y)g(y)dy$ $K:L^2(\Omeg …
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0 answers
186 views

Properties of Eigenfunctions of a Kernel

I'm a newbie and may be this question is bit simple for you but pardon me if it's too simple and provide me some references. I've and Kernel function $K(x,y)$ $f(x)=(Kg)(x)=\int_{\Omega}K(x,y)g(y)dy …
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