Linear Operators: Spectral theory |
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Page 1650
... subset I of E " . Then the closed set Cp in I which is the complement in I of the largest open set in I in which F vanishes , i.e. , which is the complement in I of the union of all the open subsets of I in which F vanishes , is called ...
... subset I of E " . Then the closed set Cp in I which is the complement in I of the largest open set in I in which F vanishes , i.e. , which is the complement in I of the union of all the open subsets of I in which F vanishes , is called ...
Page 1662
... subset of the interior of C , and let F be in D ( I ) . Suppose that F has a carrier C which is a compact subset of I. Then there is a unique distribution G in D ( C ) such that F = GI and CG = Cp . In later sections , the distribution ...
... subset of the interior of C , and let F be in D ( I ) . Suppose that F has a carrier C which is a compact subset of I. Then there is a unique distribution G in D ( C ) such that F = GI and CG = Cp . In later sections , the distribution ...
Page 1669
... subset of I , whenever C is a compact subset of I2 ; Then ( b ) ( M ( ) ) , e C ( I1 ) , j = 1 , ... , No. 2 . in ( i ) for each in C ( I2 ) , 9 M will denote the function Y C ( I ) defined , for x in I , by the equation ( x ) = q ( M ...
... subset of I , whenever C is a compact subset of I2 ; Then ( b ) ( M ( ) ) , e C ( I1 ) , j = 1 , ... , No. 2 . in ( i ) for each in C ( I2 ) , 9 M will denote the function Y C ( I ) defined , for x in I , by the equation ( x ) = q ( M ...
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