Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1420
... zero leading coefficient , ( A ) the Hilbert spaces D ( T1 ( T + T ' ) ) and D ( T1 ( t ) ) have the same elements ... zero in the topology of D ( T1 ( 7 ) ) . Then , by assumption ( b ) , { f } converges to zero in the topology of D ...
... zero leading coefficient , ( A ) the Hilbert spaces D ( T1 ( T + T ' ) ) and D ( T1 ( t ) ) have the same elements ... zero in the topology of D ( T1 ( 7 ) ) . Then , by assumption ( b ) , { f } converges to zero in the topology of D ...
Page 1432
... zero for 0≤ x ≤ n , and where we suppose that is minimal ; i.e. , that the differential equation [ * ] does not have the form Σo Bx ( t ) t − μ ( n − k ) f ( k ) ( z ) = 0 where ẞ is analytic in the neighborhood of zero for 0 ≤ k ...
... zero for 0≤ x ≤ n , and where we suppose that is minimal ; i.e. , that the differential equation [ * ] does not have the form Σo Bx ( t ) t − μ ( n − k ) f ( k ) ( z ) = 0 where ẞ is analytic in the neighborhood of zero for 0 ≤ k ...
Page 1727
... zero . Suppose that we let I , denote the cube I。= { x € E " || x , | ≤ 1 , i = 1 , ... , n } . Then for k≤ min ... zero and if -k ≤ min ( L ) ≤ max ( L ) ≤ k - 1 . In the same way we see , using ( 6 ) and ( 7 ) , that SL vanishes ...
... zero . Suppose that we let I , denote the cube I。= { x € E " || x , | ≤ 1 , i = 1 , ... , n } . Then for k≤ min ... zero and if -k ≤ min ( L ) ≤ max ( L ) ≤ k - 1 . In the same way we see , using ( 6 ) and ( 7 ) , that SL vanishes ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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