Linear Operators: Spectral theory |
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Page 1845
... spaces of continuous functions over a compact space . Amer . J. Math . 71 , 701-705 ( 1949 ) . A theorem of the Hahn - Banach ... spaces and of functions on uniform spaces . Osaka Math . J. 1 , 166-181 ( 1949 ) . Nagumo , M. 1. Einige ...
... spaces of continuous functions over a compact space . Amer . J. Math . 71 , 701-705 ( 1949 ) . A theorem of the Hahn - Banach ... spaces and of functions on uniform spaces . Osaka Math . J. 1 , 166-181 ( 1949 ) . Nagumo , M. 1. Einige ...
Page 1858
... Banach spaces . Duke Math . J. 15 , 421-431 ( 1948 ) . Mapping degree in Banach spaces and spectral theory . Math . Z. 63 , 195–218 ( 1955 ) . Rubin , H. , and Stone , M. H. 1 . Postulates for generalizations of Hilbert space . Proc ...
... Banach spaces . Duke Math . J. 15 , 421-431 ( 1948 ) . Mapping degree in Banach spaces and spectral theory . Math . Z. 63 , 195–218 ( 1955 ) . Rubin , H. , and Stone , M. H. 1 . Postulates for generalizations of Hilbert space . Proc ...
Page 1869
... Banach spaces whose elements are analytic functions . Actas Acad . Ci . Lima 12 , 31-43 ( 1949 ) . Weak convergence in the space H. Duke Math . J. 17 , 409–418 ( 1950 ) . New proofs of some theorems of Hardy by Banach space methods ...
... Banach spaces whose elements are analytic functions . Actas Acad . Ci . Lima 12 , 31-43 ( 1949 ) . Weak convergence in the space H. Duke Math . J. 17 , 409–418 ( 1950 ) . New proofs of some theorems of Hardy by Banach space methods ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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