Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1162
... obtained by Wermer [ 7 ] who determined the primary ideals in some of these algebras . Other results of a related nature have been obtained by Beurling [ 2 ] , [ 3 ] . Fredholm theory . Location of eigenvalues . The Fredholm theory of ...
... obtained by Wermer [ 7 ] who determined the primary ideals in some of these algebras . Other results of a related nature have been obtained by Beurling [ 2 ] , [ 3 ] . Fredholm theory . Location of eigenvalues . The Fredholm theory of ...
Page 1327
... obtained from 7 by imposing a real symmetric set of boundary con- ditions , a further simplification can be obtained by noticing that the solutions of the equation ( 7 * —Ã ) σ = 0 are complex conjugates of the solutions of the ...
... obtained from 7 by imposing a real symmetric set of boundary con- ditions , a further simplification can be obtained by noticing that the solutions of the equation ( 7 * —Ã ) σ = 0 are complex conjugates of the solutions of the ...
Page 1624
... obtained from the operator enjoy the property ∞ ∞ cos s√λ cos t√Ãμ ( dλ ) = 0 , st . Making use of these relations , Gelfand and Levitan attempt to reconstruct the functions f ( t , 2 ) by " orthogonalizing " the functions cos t ...
... obtained from the operator enjoy the property ∞ ∞ cos s√λ cos t√Ãμ ( dλ ) = 0 , st . Making use of these relations , Gelfand and Levitan attempt to reconstruct the functions f ( t , 2 ) by " orthogonalizing " the functions cos t ...
Contents
IX | 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 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