Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1343
... sufficiently close to 2 , σ ( M ( 2 ) ) ◇ U is non - void . Thus if n ( 2 ) denotes the number of distinct points in the spectrum of M ( 2 ) , the sets { λ € σn ( 1 ) ≥ s } are relatively open in σ , and hence the sets b ̧ = { λ = σ ...
... sufficiently close to 2 , σ ( M ( 2 ) ) ◇ U is non - void . Thus if n ( 2 ) denotes the number of distinct points in the spectrum of M ( 2 ) , the sets { λ € σn ( 1 ) ≥ s } are relatively open in σ , and hence the sets b ̧ = { λ = σ ...
Page 1414
... sufficiently near b , and ( b ) for x sufficiently near b , We conclude that יך ' ( ( q ( t ) ( q ( t ) ) 3/2 ( a ) if for all x , [ ( q ( t ) ) ' ] 2 + 4 dt < ∞ ( q ( t ) ) 5/2 S 19 ( 1 ) 1-1 / 2dt then τ has no boundary values at b ...
... sufficiently near b , and ( b ) for x sufficiently near b , We conclude that יך ' ( ( q ( t ) ( q ( t ) ) 3/2 ( a ) if for all x , [ ( q ( t ) ) ' ] 2 + 4 dt < ∞ ( q ( t ) ) 5/2 S 19 ( 1 ) 1-1 / 2dt then τ has no boundary values at b ...
Page 1760
... sufficiently small positive a ≤a ( k ) , the mapping I - ¿ S , has a range dense in Â1⁄4 ( C ) . k π Suppose that ( v ) is false , but that ( vii ) has been established . Since ( v ) is false , and since D ( S ) = D ( W ) , there ...
... sufficiently small positive a ≤a ( k ) , the mapping I - ¿ S , has a range dense in Â1⁄4 ( C ) . k π Suppose that ( v ) is false , but that ( vii ) has been established . Since ( v ) is false , and since D ( S ) = D ( W ) , there ...
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