All Questions
Tagged with hermitian fa.functional-analysis
5 questions
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Spectral theorem and diagonal expansion for self adjoint operators
Asked by a physicist:
In physics we use the fact that, given a self adjoint operator $A$, every element in Hilbert space can be written as "generalized linear combination" of the eigenstates ...
1
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1
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133
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Embedding Hermitian forms into Hilbert spaces
Let $H$ be a nondegenerate, not positive definite, Hermitian form on a complex vector space $V$ such that
$$|H(x,y)|\le u(x)u(y)\tag{B}$$
for some map $u:V\to R_+$ with $u(\lambda x)=|\lambda|u(x)$ ...
0
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0
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113
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References for a proof or interpretation of deficiency indices theorem (von Neumann)
I am looking for a proof or some interpretation around why the domain of the new extension $D(A_U)$ in the Theorem below is given by its specific formula.
I have already searched in papers and here ...
2
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0
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219
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Integral with product of two infinite sums
I am looking for references and results on integrals with product of two infinite sums:
$$S_1=\int_0^{\infty} \sum_{n=0}^{\infty} f(nx) \sum_{k=0}^{\infty} \overline{ g(kx)} dx$$
Above integral is ...
1
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1
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231
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Hermitian Projections on $C[0,1]$
If $X$ is a normed linear space and $S(X)$ its unit sphere, $X′$ its dual space and $Π=\{(x,f)∈S(X)×S(X′) \ | \ f(x)=1\}$, then for an operator $T$ on $X$, the numerical range $V(T)$ is defined by $V(...