Linear Operators: Spectral theory |
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Page 978
... Closure Theorems As in the preceding section the letter R will stand for a non- discrete locally compact Abelian group and integration will always be performed with respect to a Haar measure on the group . It was observed in Corollary ...
... Closure Theorems As in the preceding section the letter R will stand for a non- discrete locally compact Abelian group and integration will always be performed with respect to a Haar measure on the group . It was observed in Corollary ...
Page 993
... closure . Then it follows from what has just been demonstrated that av , ay , i.e. , ap is independent of V. Q.E.D. ... closure we have ( i ) τφτίχν = χν · Since every compact set in R is contained in an open set with compact closure it ...
... closure . Then it follows from what has just been demonstrated that av , ay , i.e. , ap is independent of V. Q.E.D. ... closure we have ( i ) τφτίχν = χν · Since every compact set in R is contained in an open set with compact closure it ...
Page 1226
... closure , and written T. 8 LEMMA . ( a ) The closure T of T is the restriction of T * to the closure of D ( T ) in the Hilbert space D ( T * ) . ( b ) The operator T and its closure have the same closed extensions . ( c ) The operator T ...
... closure , and written T. 8 LEMMA . ( a ) The closure T of T is the restriction of T * to the closure of D ( T ) in the Hilbert space D ( T * ) . ( b ) The operator T and its closure have the same closed extensions . ( c ) The operator T ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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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