Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1133
... interval of the complement of C. Conversely , if the kernels K ,, have this property , then F is a maximal family of subdiagonalizing orthogonal projections for T. Moreover , T is a quasi - nilpotent operator if and only if K11 ( s , t ) ...
... interval of the complement of C. Conversely , if the kernels K ,, have this property , then F is a maximal family of subdiagonalizing orthogonal projections for T. Moreover , T is a quasi - nilpotent operator if and only if K11 ( s , t ) ...
Page 1279
... interval of the real axis . The interval I can be open , half - open , or closed . The interval ( a , c ) is considered to be half - open ; the interval ( ∞ , ∞ ) to be open . Thus a closed interval is a compact set . An end point t ...
... interval of the real axis . The interval I can be open , half - open , or closed . The interval ( a , c ) is considered to be half - open ; the interval ( ∞ , ∞ ) to be open . Thus a closed interval is a compact set . An end point t ...
Page 1599
... interval [ 0 , ∞ ) . Then on the positive real axis every interval of length K contains a point of the essential spectrum of τ ( Glazman [ 4 ] , Exercise 9.A 6 ) . ( 32 ) On the interval [ 0 , ∞ ) , if q ( t ) tends monotonically to ...
... interval [ 0 , ∞ ) . Then on the positive real axis every interval of length K contains a point of the essential spectrum of τ ( Glazman [ 4 ] , Exercise 9.A 6 ) . ( 32 ) On the interval [ 0 , ∞ ) , if q ( t ) tends monotonically to ...
Contents
IX | 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 compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain 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 isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero