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Results tagged with fa.functional-analysis
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user 22815
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
7
votes
0
answers
3k
views
Definition of homogeneous Sobolev spaces
As we know the inhomogeneous Sobolev space (we only consider $s>0$)
$${H}^{s}\left(\mathbb{R}^{n}\right)=\left\{f \in L^2(\mathbb{R}^n):\int_{\mathbb{R}^{n}}|\xi|^{2 s}|\hat{f}(\xi)|^{2} \mathrm{d} \x …
- 633
1
vote
1
answer
169
views
Inverse of holomorphic elliptic differential operator
Consider the Beltrami-Laplacian $\Delta$ on $\mathbb{S}^n$ with standard metric. One can define a family of operators $A(z):H^1(\mathbb{S}^n)\to H^1(\mathbb{S}^n)$ as the following
$$A(z)=\Delta+z$$
T …
- 633