Linear Operators: Spectral theory |
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Page 1802
... Math . ( 2 ) 51 , 387-408 ( 1950 ) . Sur certains espaces considérés par M. H. Stone . Summa Brasil . Math . 2 , 151-182 ( 1951 ) . Sur un théorème de Banach . Duke Math . J. 15 , 1057–1071 ( 1948 ) . Les algèbres d'opérateurs dans l ...
... Math . ( 2 ) 51 , 387-408 ( 1950 ) . Sur certains espaces considérés par M. H. Stone . Summa Brasil . Math . 2 , 151-182 ( 1951 ) . Sur un théorème de Banach . Duke Math . J. 15 , 1057–1071 ( 1948 ) . Les algèbres d'opérateurs dans l ...
Page 1809
... Math . 6 , 299-326 ( 1953 ) . Mathematical aspects of the quantum theory of fields . Interscience Pub . , New York ... Duke Math . J. 13 , 269-280 ( 1946 ) . 3 . 4 . The representation of linear operators from L ' to L. Proc . Amer ...
... Math . 6 , 299-326 ( 1953 ) . Mathematical aspects of the quantum theory of fields . Interscience Pub . , New York ... Duke Math . J. 13 , 269-280 ( 1946 ) . 3 . 4 . The representation of linear operators from L ' to L. Proc . Amer ...
Page 1856
... Duke Math . J. 14 , 1063–1077 ( 1947 ) . Isomorphic groups of linear transformations . Amer . J. Math . 72 , 451-464 ( 1950 ) . Banach algebras with an adjoint operation . Ann . of Math . ( 2 ) 47 , 528–550 ( 1946 ) . The uniqueness of ...
... Duke Math . J. 14 , 1063–1077 ( 1947 ) . Isomorphic groups of linear transformations . Amer . J. Math . 72 , 451-464 ( 1950 ) . Banach algebras with an adjoint operation . Ann . of Math . ( 2 ) 47 , 528–550 ( 1946 ) . The uniqueness of ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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59 other sections not shown
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 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 real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T unique unitary vanishes vector zero