Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
From inside the book
Results 1-3 of 84
Page 1191
... adjoint of id / dt . The problem , suggested by the preceding example , of finding self adjoint extensions of a given symmetric operator will be treated systematically in Section 4 . 2. The Spectral Theorem for Unbounded Self Adjoint ...
... adjoint of id / dt . The problem , suggested by the preceding example , of finding self adjoint extensions of a given symmetric operator will be treated systematically in Section 4 . 2. The Spectral Theorem for Unbounded Self Adjoint ...
Page 1290
... adjoint provided only that the coefficients p are real . In the same way , the formal differential operator ( i / 2 ) ( d / dt ) " { p ( t ) ( d / dt ) + ( d / dt ) p ( t ) } ( d / dt ) " is formally self adjoint provided that p ( t ) ...
... adjoint provided only that the coefficients p are real . In the same way , the formal differential operator ( i / 2 ) ( d / dt ) " { p ( t ) ( d / dt ) + ( d / dt ) p ( t ) } ( d / dt ) " is formally self adjoint provided that p ( t ) ...
Page 1548
... adjoint operators T and Î as in Exercise D2 . Show that „ ( T ) ≥ ¡ „ ( Î ) , n ≥ 1 . 1 D11 Let T1 be a self adjoint operator in Hilbert space 1 , and let T2 be a self adjoint operator in Hilbert space 2. Define the operator T in S 12 ...
... adjoint operators T and Î as in Exercise D2 . Show that „ ( T ) ≥ ¡ „ ( Î ) , n ≥ 1 . 1 D11 Let T1 be a self adjoint operator in Hilbert space 1 , and let T2 be a self adjoint operator in Hilbert space 2. Define the operator T in S 12 ...
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