Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1310
... square - integrable at a and satisfying the boundary conditions at a , and exactly one solution y ( t , λ ) of ( t −λ ) y = 0 square - integrable at b and satisfying the boundary conditions at b . - PROOF . We shall show the theorem is ...
... square - integrable at a and satisfying the boundary conditions at a , and exactly one solution y ( t , λ ) of ( t −λ ) y = 0 square - integrable at b and satisfying the boundary conditions at b . - PROOF . We shall show the theorem is ...
Page 1329
... square - integrable at a and satisfying the boundary conditions at a , and exactly one solution y ( t , 2 ) of ( x - 2 ) σ = 0 square- integrable at b satisfying the boundary conditions at b . The resolvent R ( A ; T ) is an integral ...
... square - integrable at a and satisfying the boundary conditions at a , and exactly one solution y ( t , 2 ) of ( x - 2 ) σ = 0 square- integrable at b satisfying the boundary conditions at b . The resolvent R ( A ; T ) is an integral ...
Page 1563
... square - integrable . Prove that the positive real axis belongs to the essential spectrum of the operator τ . ( Hint : Say there is a square - integrable f such that ( 1 - T ) = 0 , where λ > 0 , and let g1 ( t ) and g2 ( t ) be ...
... square - integrable . Prove that the positive real axis belongs to the essential spectrum of the operator τ . ( Hint : Say there is a square - integrable f such that ( 1 - T ) = 0 , where λ > 0 , and let g1 ( t ) and g2 ( t ) be ...
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