Linear Operators, Part 2 |
From inside the book
Results 1-3 of 74
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
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
57 other sections not shown
Other editions - View all
Common terms and phrases
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