Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 69
Page 1817
... linear differential equations of second order . Amer . J. Math . 70 , 1–10 ( 1948 ) . Criteria for the non - degeneracy of the wave equation . Amer . J. Math . 70 , 295-308 ( 1948 ) . On the orientation of unilateral spectra . Amer . J ...
... linear differential equations of second order . Amer . J. Math . 70 , 1–10 ( 1948 ) . Criteria for the non - degeneracy of the wave equation . Amer . J. Math . 70 , 295-308 ( 1948 ) . On the orientation of unilateral spectra . Amer . J ...
Page 1852
... linear transformations . Proc . Amer . Math . Soc . 2 , 234-237 ( 1951 ) . Semi - groups of operators . Bull . Amer . Math . Soc . 61 , 16-33 ( 1955 ) . An inversion formula for Laplace transforms and semi - groups of linear operators ...
... linear transformations . Proc . Amer . Math . Soc . 2 , 234-237 ( 1951 ) . Semi - groups of operators . Bull . Amer . Math . Soc . 61 , 16-33 ( 1955 ) . An inversion formula for Laplace transforms and semi - groups of linear operators ...
Page 1912
... Linear dimension , ( 91 ) Linear functional , ( 38 ) . ( See also Functional ) Linear manifold , ( 36 ) . ( See also Mani- fold ) Linear operator , ( 36 ) . ( See also B- space ) Linear space , I.11 normed , II.3.1 ( 59 ) . ( See also B ...
... Linear dimension , ( 91 ) Linear functional , ( 38 ) . ( See also Functional ) Linear manifold , ( 36 ) . ( See also Mani- fold ) Linear operator , ( 36 ) . ( See also B- space ) Linear space , I.11 normed , II.3.1 ( 59 ) . ( See also B ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
52 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 Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero