Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 84
Page 1224
... symmetric extension of a symmetric operator T with dense domain , we have only to restrict T * to some suitably chosen subdomain of D ( T * ) . Keeping this basic principle firmly in mind , we embark upon a systematic study of the ...
... symmetric extension of a symmetric operator T with dense domain , we have only to restrict T * to some suitably chosen subdomain of D ( T * ) . Keeping this basic principle firmly in mind , we embark upon a systematic study of the ...
Page 1238
... symmetric operator with finite deficiency indices whose sum is p . Let A1 , ... , A , be a complete set of boundary values for T , and let Σ3‚ ̧¡ – 1¤¡¡Â¿Ã¡ be the bilinear form of Lemma 23 . A set of boundary conditions 1P , A ̧ ( x ) ...
... symmetric operator with finite deficiency indices whose sum is p . Let A1 , ... , A , be a complete set of boundary values for T , and let Σ3‚ ̧¡ – 1¤¡¡Â¿Ã¡ be the bilinear form of Lemma 23 . A set of boundary conditions 1P , A ̧ ( x ) ...
Page 1272
... symmetric operators . If T is a symmetric operator with dense domain , then it has proper symmetric extensions provided both of its deficiency indices are different from zero . A maximal symmetric operator is one which has no proper ...
... symmetric operators . If T is a symmetric operator with dense domain , then it has proper symmetric extensions provided both of its deficiency indices are different from zero . A maximal symmetric operator is one which has no proper ...
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