Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 87
Page 993
... follows from what has just been demonstrated that av , ay , i.e. , ap is independent of V. Q.E.D. av 1 = = ayuvi 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 , ay , i.e. , ap is independent of V. Q.E.D. av 1 = = ayuvi 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 ( ƒ * q ) ≤ o ( p ) and from Lemma 12 ( c ) and the equation f = tf it follows that o ( ƒ * q ) contains no interior point of o ( q ) . Hence o ( ƒ * q ) ...
... follows from the above equation that f * q0 . From Lemma 12 ( b ) it is seen that o ( ƒ * q ) ≤ o ( p ) and from Lemma 12 ( c ) and the equation f = tf it follows that o ( ƒ * q ) contains no interior point of o ( q ) . Hence o ( ƒ * q ) ...
Page 1708
... follows that there exists some F in H ( + ) such that ( T1 + σɛ ) F = gɛ • However , since fɛy is in H ( m + -1 ) , and since by ( 5 ) , ( T1 + oε ) fe = 8ε , it follows that fep F is in Hm + P ) ( C ) so that a fortiori , fe is in Am + ...
... follows that there exists some F in H ( + ) such that ( T1 + σɛ ) F = gɛ • However , since fɛy is in H ( m + -1 ) , and since by ( 5 ) , ( T1 + oε ) fe = 8ε , it follows that fep F is in Hm + P ) ( C ) so that a fortiori , fe is in Am + ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
37 other sections not shown
Other editions - View all
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero