Linear Operators: Spectral theory |
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Page 1348
... solutions of to λo . However , in the range λ < 0 , 2 is imaginary , and an analytic expression like cost is hard to ... solutions of to λσ is ô1 ( t , λ ) = ô1⁄2 ( t , λ ) = et√Fλ Το = τσ = Of course , as long as we are dealing with ...
... solutions of to λo . However , in the range λ < 0 , 2 is imaginary , and an analytic expression like cost is hard to ... solutions of to λσ is ô1 ( t , λ ) = ô1⁄2 ( t , λ ) = et√Fλ Το = τσ = Of course , as long as we are dealing with ...
Page 1392
... solutions of τσ 2o is by no means trivial . If , for instance , we take ( d / dt ) 2 + t2 , then the solutions of to λo are particular confluent hypergeometric functions . Because of the difficulty of dealing with the various functions ...
... solutions of τσ 2o is by no means trivial . If , for instance , we take ( d / dt ) 2 + t2 , then the solutions of to λo are particular confluent hypergeometric functions . Because of the difficulty of dealing with the various functions ...
Page 1632
... solution for each set of prescribed , smooth initial data . Property B : The solutions of Lf 0 are so smooth as to be subject to the function - theoretic principle of unique continuation . Formal partial differential operators with ...
... solution for each set of prescribed , smooth initial data . Property B : The solutions of Lf 0 are so smooth as to be subject to the function - theoretic principle of unique continuation . Formal partial differential operators with ...
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