Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1338
... respect to a positive o - finite measure μ . If the matrix of densities { m } is defined by the equations μ ,, ( 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 μ ,, ( 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 the matrix of densities of the with respect to the measure ( μ + μ ) . If m is the density of u with respect ...
... respect to which the set functions μ , are continuous . Let { m } be the corresponding matrix of densities , and let { n , } be the matrix of densities of the with respect to the measure ( μ + μ ) . If m is the density of u with respect ...
Page 1738
... respect to r , that ↓↓ _h ( x ) { g ( x ) dx = ( −1 ) 3 С , ? h ( x ) g ( x ) dx + + 1 for all g in Co ( V ) and h in Co ( V ) , and it follows by continuity , since Co ( V ) is by definition of H ( V ) dense in Hg ( V ) , that this ...
... respect to r , that ↓↓ _h ( x ) { g ( x ) dx = ( −1 ) 3 С , ? h ( x ) g ( x ) dx + + 1 for all g in Co ( V ) and h in Co ( V ) , and it follows by continuity , since Co ( V ) is by definition of H ( V ) dense in Hg ( V ) , that this ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise 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 isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero