Linear Operators: Spectral theory |
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Page 950
... compact Abelian group which we denote by R. We assume throughout that R is o - compact , i.e. , the union of countably many compact sets . Every such group has a non - negative countably additive measure which is defined on the Borel ...
... compact Abelian group which we denote by R. We assume throughout that R is o - compact , i.e. , the union of countably many compact sets . Every such group has a non - negative countably additive measure which is defined on the Borel ...
Page 1150
... compact , o - compact Abelian group . However , there are a few comments that we should make con- cerning the general non - Abelian case . First of all we shall prove , in Theorem 2 , that a locally compact group is automatically a ...
... compact , o - compact Abelian group . However , there are a few comments that we should make con- cerning the general non - Abelian case . First of all we shall prove , in Theorem 2 , that a locally compact group is automatically a ...
Page 1331
... compact . This is a special case of Exercise VI.9.52 , but , for the sake of completeness , a proof will be given here . Note first , that by Schwarz ' inequality , dt √ , \ S , K ... COMPACT RESOLVENTS Spectral Theory: Compact Resolvents.
... compact . This is a special case of Exercise VI.9.52 , but , for the sake of completeness , a proof will be given here . Note first , that by Schwarz ' inequality , dt √ , \ S , K ... COMPACT RESOLVENTS Spectral Theory: Compact Resolvents.
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero