Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1164
... satisfies a suitable , rather weak , continuity hypothesis , then the singular integral q ( x ) = S Q ( x - y ) f ... satisfies s1 \ p ( x ) \ 1 − ε dx < ∞ if ƒ € L1 ( E ” ) , ɛ > 0 , and A is bounded ; ( iii ) satisfies { √ ( x ) ...
... satisfies a suitable , rather weak , continuity hypothesis , then the singular integral q ( x ) = S Q ( x - y ) f ... satisfies s1 \ p ( x ) \ 1 − ε dx < ∞ if ƒ € L1 ( E ” ) , ɛ > 0 , and A is bounded ; ( iii ) satisfies { √ ( x ) ...
Page 1385
... satisfies the boundary condition f ( 0 ) + kf ' ( 0 ) if and only if 1 - k√λ = 0 ; i.e. , if and only if k is positive and λ = -1 / k2 . Thus , only in case ( iv ) does T have a non - void point spectrum , which consists of the single ...
... satisfies the boundary condition f ( 0 ) + kf ' ( 0 ) if and only if 1 - k√λ = 0 ; i.e. , if and only if k is positive and λ = -1 / k2 . Thus , only in case ( iv ) does T have a non - void point spectrum , which consists of the single ...
Page 1460
... satisfies Tf = 2 ; f . Since by Theorem 2.10 and Lemma XII.4.1 ( b ) , Tf λf implies T1 ( T ) = λf , it follows that E ( L ( I ) ) is finite dimensional for each i = 1 , ... , p . We may , consequently , find finite orthonormal 1 ...
... satisfies Tf = 2 ; f . Since by Theorem 2.10 and Lemma XII.4.1 ( b ) , Tf λf implies T1 ( T ) = λf , it follows that E ( L ( I ) ) is finite dimensional for each i = 1 , ... , p . We may , consequently , find finite orthonormal 1 ...
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