Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 993
... follows from what has just been demonstrated that av , = αvuv , ay , i.e. , ap is independent of V. Q.E.D. ато 1 ... follows from Lemma 3.6 that equation ( i ) holds for any open set with finite measure . It follows from the regularity ...
... follows from what has just been demonstrated that av , = αvuv , ay , i.e. , ap is independent of V. Q.E.D. ато 1 ... follows from Lemma 3.6 that equation ( i ) holds for any open set with finite measure . It follows from the regularity ...
Page 996
... follows from the above equation that f * q0 . From Lemma 12 ( b ) it is seen that o ( f * y ) Co ( y ) and from Lemma 12 ( c ) and the equation Tƒ = tf it follows that o ( ƒ * q ) contains no interior point of o ( q ) . Hence σ ( ƒ * q ) ...
... follows from the above equation that f * q0 . From Lemma 12 ( b ) it is seen that o ( f * y ) Co ( y ) and from Lemma 12 ( c ) and the equation Tƒ = tf it follows that o ( ƒ * q ) contains no interior point of o ( q ) . Hence σ ( ƒ * q ) ...
Page 1708
... follows that there exists some F in H ( m + ) such that ( T1 + 0g ) F = gg . However , since fee is in Hm + -1 ) , and since by ( 5 ) , ( T1 + 0 ) fε = ge , it follows that fe F is in Hm + ) ( C ) so that a fortiori , fe is in Am + P ...
... follows that there exists some F in H ( m + ) such that ( T1 + 0g ) F = gg . However , since fee is in Hm + -1 ) , and since by ( 5 ) , ( T1 + 0 ) fε = ge , it follows that fe F is in Hm + ) ( C ) so that a fortiori , fe is in Am + P ...
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