Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 52
Page 1338
... respect to a positive o - finite measure μ . If the matrix of densities { m } is defined by the equations M1 , ( e ) ... respect to which all the set functions μ ,, are absolutely continuous . If { m } denotes the matrix of densities of ...
... respect to a positive o - finite measure μ . If the matrix of densities { m } is defined by the equations M1 , ( e ) ... respect to which all the set functions μ ,, are absolutely continuous . If { m } denotes the matrix of densities of ...
Page 1340
... respect to which the set functions μ , are continuous . Let { m } be the corresponding matrix of densities , and let { n , } be with respect to the measure ( u + μ ) . If m is the density of u with respect to ( u + μ ) , then the matrix ...
... respect to which the set functions μ , are continuous . Let { m } be the corresponding matrix of densities , and let { n , } be with respect to the measure ( u + μ ) . If m is the density of u with respect to ( u + μ ) , then the matrix ...
Page 1738
... respect to x1 Sy_h ( x ) { g ( x ) dx ( −1 ) 3 √ √ ph ( x ) g ( x ) dx that for all g in Co ( V ) and h in CP ( V ) , and it follows by continuity , since CO ( V ) is by definition of Hg ( V ) dense in Hg ( V ) , that this identity ...
... respect to x1 Sy_h ( x ) { g ( x ) dx ( −1 ) 3 √ √ ph ( x ) g ( x ) dx that for all g in Co ( V ) and h in CP ( V ) , and it follows by continuity , since CO ( V ) is by definition of Hg ( V ) dense in Hg ( V ) , that this identity ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
37 other sections not shown
Other editions - View all
Common terms and phrases
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