Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 81
Page 861
... linear map of one B - space onto another B - space which has a continuous inverse . The closed graph theorem ( II.2.4 ) shows that t is a homeomorphism . Thus the algebra X is topologically and algebraically equivalent to the B ...
... linear map of one B - space onto another B - space which has a continuous inverse . The closed graph theorem ( II.2.4 ) shows that t is a homeomorphism . Thus the algebra X is topologically and algebraically equivalent to the B ...
Page 1221
... continuous linear functionals y , ... , y , in La ( Sm , E , v ) such that y ( W , ( , 0 ) ) = 8 ,,, i = 1 , ... , p - 1 . Define the continuous * = y * ( f \ Sm ) for dij XII.3.19 SPECTRAL REPRESENTATION OF TRANSFORMATIONS 1221.
... continuous linear functionals y , ... , y , in La ( Sm , E , v ) such that y ( W , ( , 0 ) ) = 8 ,,, i = 1 , ... , p - 1 . Define the continuous * = y * ( f \ Sm ) for dij XII.3.19 SPECTRAL REPRESENTATION OF TRANSFORMATIONS 1221.
Page 1903
... continuous linear functionals , V.7.3 ( 436 ) non - existence in L ,, 0 < p < 1 , V.7.37 ( 438 ) Continuous functions . ( See also Abso- lutely continuous functions ) as a B - space , additional properties , IV.15 definition , IV.2.14 ...
... continuous linear functionals , V.7.3 ( 436 ) non - existence in L ,, 0 < p < 1 , V.7.37 ( 438 ) Continuous functions . ( See also Abso- lutely continuous functions ) as a B - space , additional properties , IV.15 definition , IV.2.14 ...
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