Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 79
Page 1130
... kernel K ( a , b ) , then the adjoint operator K * is represented by the kernel K ( b , a ) . Conversely , if K ( · , · ) is a kernel satisfying ( 1 ) , then ( 2 ) defines a Hilbert - Schmidt operator . To prove these assertions , let ...
... kernel K ( a , b ) , then the adjoint operator K * is represented by the kernel K ( b , a ) . Conversely , if K ( · , · ) is a kernel satisfying ( 1 ) , then ( 2 ) defines a Hilbert - Schmidt operator . To prove these assertions , let ...
Page 1131
... kernel representing K * is the function K ( b , a ) = K * ( a , b ) with the Fourier coefficients C If K ( a , b ) is a kernel satisfying the inequality in ( 1 ) , then we have seen that the right side of ( 2 ) defines a bounded ...
... kernel representing K * is the function K ( b , a ) = K * ( a , b ) with the Fourier coefficients C If K ( a , b ) is a kernel satisfying the inequality in ( 1 ) , then we have seen that the right side of ( 2 ) defines a bounded ...
Page 1590
... kernel for an operator of the second order on a compact interval is a kernel of the Hilbert - Schmidt type . As soon as the results of Hilbert and E. Schmidt on such an integral kernel became available , the idea of obtaining the ...
... kernel for an operator of the second order on a compact interval is a kernel of the Hilbert - Schmidt type . As soon as the results of Hilbert and E. Schmidt on such an integral kernel became available , the idea of obtaining the ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
45 other sections not shown
Other editions - View all
Common terms and phrases
A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero