Linear Operators: Spectral theory |
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Page 1529
... solution whose asymp- totic expansion begins with the factor exp ( ¿ 1 ) 2−1 ) . Thus , a solution ( " small solution " ) with the first kind of asymptotic expansion is uniquely determined by its asymptotic expansion ; while a solution ...
... solution whose asymp- totic expansion begins with the factor exp ( ¿ 1 ) 2−1 ) . Thus , a solution ( " small solution " ) with the first kind of asymptotic expansion is uniquely determined by its asymptotic expansion ; while a solution ...
Page 1553
... solution of the equation ( 2-7 ) 0. Prove : = ( a ) either f is square - integrable , or the point 2 belongs to the essential spectrum of t ; ( b ) if all solutions of the equation ( 2-7 ) f = 0 are bounded , then belongs to the ...
... solution of the equation ( 2-7 ) 0. Prove : = ( a ) either f is square - integrable , or the point 2 belongs to the essential spectrum of t ; ( b ) if all solutions of the equation ( 2-7 ) f = 0 are bounded , then belongs to the ...
Page 1556
... solution of the above equation ? G14 Use the result of the preceding exercise to show that if the operator has two boundary values at infinity , then N ( t ) lim t2 t → ∞ = ∞ , where N ( t ) is the number of zeros of a solution of ...
... solution of the above equation ? G14 Use the result of the preceding exercise to show that if the operator has two boundary values at infinity , then N ( t ) lim t2 t → ∞ = ∞ , where N ( t ) is the number of zeros of a solution of ...
Contents
BAlgebras | 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 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