Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 993
... follows from what has just been demonstrated that ay , ayuv1 ay , i.e. , ap is independent of V. Q.E.D. 0 = = 16 ... 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 ay , ayuv1 ay , i.e. , ap is independent of V. Q.E.D. 0 = = 16 ... 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 * 90 . From Lemma 12 ( b ) it is seen that o ( ƒ * y ) Co ( y ) and from Lemma 12 ( c ) and the equation T Tf it follows that o ( f * q ) contains no interior point of ( q ) . Hence σ ( ƒ * q ) is ...
... follows from the above equation that f * 90 . From Lemma 12 ( b ) it is seen that o ( ƒ * y ) Co ( y ) and from Lemma 12 ( c ) and the equation T Tf it follows that o ( f * q ) contains no interior point of ( q ) . Hence σ ( ƒ * q ) is ...
Page 1708
... follows that there exists some F in H + ) such that ( T1 + σ € ) F = gɛ . However , since fe is in Hm + 1 ) , and since by ( 5 ) , ( T1 + 0 ) fe ? = 8e , it follows that fe = F is in Hm + P ) ( C ) so that a fortiori , fɛ is in Am + ...
... follows that there exists some F in H + ) such that ( T1 + σ € ) F = gɛ . However , since fe is in Hm + 1 ) , and since by ( 5 ) , ( T1 + 0 ) fe ? = 8e , it follows that fe = F is in Hm + P ) ( C ) so that a fortiori , fɛ is in Am + ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum 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(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero