Linear Operators: Spectral theory |
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Page 1529
The confluent hypergeometric equation has the characteristic equation a2 = 0 , so that 11 ) = 0,5 ) = 1. Thus the Stokes lines - a ( 1 ) for this equation are the positive and negative imaginary axes . Trying solutions of the form z ...
The confluent hypergeometric equation has the characteristic equation a2 = 0 , so that 11 ) = 0,5 ) = 1. Thus the Stokes lines - a ( 1 ) for this equation are the positive and negative imaginary axes . Trying solutions of the form z ...
Page 1553
G3 Suppose that the operator t has the property that for some à the derivative of every square - integrable solution of the equation ( 1-1 ) } = 0 is bounded . Prove that t has no boundary values at infinity .
G3 Suppose that the operator t has the property that for some à the derivative of every square - integrable solution of the equation ( 1-1 ) } = 0 is bounded . Prove that t has no boundary values at infinity .
Page 1556
What is the relationship between 0 ( t ) and the number of zeros of a solution of the above equation ? G14 Use the result of the preceding exercise to show that if the operator t has two boundary values at infinity , then N ( t ) lim ...
What is the relationship between 0 ( t ) and the number of zeros of a solution of the above equation ? G14 Use the result of the preceding exercise to show that if the operator t has two boundary values at infinity , then N ( t ) lim ...
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Contents
8 | 876 |
859 | 885 |
extensive presentation of applications of the spectral theorem | 911 |
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additive adjoint adjoint operator algebra analytic assume basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues elements equal equation equivalent Exercise exists extension fact finite dimensional follows follows from Lemma formal differential operator formula function given Hence Hilbert space Hilbert-Schmidt ideal identity immediately implies independent inequality integral interval invariant isometric isomorphism Lemma limit linear Ly(R mapping matrix measure multiplicity neighborhood norm obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solutions spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero