Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 931
... restriction of T to M is then represented as multiplication by z on a space of analytic functions . Applications are made to the restrictions of normal and unitary operators . Halmos , Lumer , and Schäffer [ 1 ] proved that the restriction ...
... restriction of T to M is then represented as multiplication by z on a space of analytic functions . Applications are made to the restrictions of normal and unitary operators . Halmos , Lumer , and Schäffer [ 1 ] proved that the restriction ...
Page 1218
... restriction of f to the complement of o is continuous . PROOF . If the restrictions fo , gd are continuous then so is the restriction ( af + ẞg ) on 8 and thus the class of measurable functions having the required property is a linear ...
... restriction of f to the complement of o is continuous . PROOF . If the restrictions fo , gd are continuous then so is the restriction ( af + ẞg ) on 8 and thus the class of measurable functions having the required property is a linear ...
Page 1471
... restriction of T1 ( 1 ) defined by a boundary condition f ( t ) + cf ' ( t ) = 0 and by the boundary condition B ( ƒ ) = 0 ( if has any boundary values at a ) , then S * is the restriction of T1 ( 7 ) defined by the boundary condition f ...
... restriction of T1 ( 1 ) defined by a boundary condition f ( t ) + cf ' ( t ) = 0 and by the boundary condition B ( ƒ ) = 0 ( if has any boundary values at a ) , then S * is the restriction of T1 ( 7 ) defined by the boundary condition f ...
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