Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1103
... sufficiently large z . Lemma 6.22 then implies that | L ( ≈ ) | ≤ 8ɛ | z | for sufficiently large z , so that │L ( ≈ ) | lim 121 → 00 = 0 . Thus L ( x ) / z is analytic and vanishes at z = ∞ . The Laurent series of L ( 2 ) at z ...
... sufficiently large z . Lemma 6.22 then implies that | L ( ≈ ) | ≤ 8ɛ | z | for sufficiently large z , so that │L ( ≈ ) | lim 121 → 00 = 0 . Thus L ( x ) / z is analytic and vanishes at z = ∞ . The Laurent series of L ( 2 ) at z ...
Page 1343
... sufficiently close to 20 , o ( 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 e σon ( λ ) ≥ s } are relatively open in σ , and hence the sets b ̧ = { λ € σ ...
... sufficiently close to 20 , o ( 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 e σon ( λ ) ≥ s } are relatively open in σ , and hence the sets b ̧ = { λ € σ ...
Page 1475
... sufficiently small so that σ ( z , + 8 , 2 ) and σ ( z , -d , 2 ) have opposite signs . Thus , ( Lemma 42 ) for sufficiently small ɛ , σ ( z ; +8 , 2 − ɛ ) and σ ( z ; -8 , 2 - ε ) have opposite signs . But this means that o ( t , 2 ...
... sufficiently small so that σ ( z , + 8 , 2 ) and σ ( z , -d , 2 ) have opposite signs . Thus , ( Lemma 42 ) for sufficiently small ɛ , σ ( z ; +8 , 2 − ɛ ) and σ ( z ; -8 , 2 - ε ) have opposite signs . But this means that o ( t , 2 ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero