Linear Operators: Spectral theory |
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Page 1550
Prove that the o - essential spectrum of the operator t in L , ( I ) is the empty set . E8 ( Bellman ) Suppose that every solution of the equation tf = 0 is of class L , ( 1 ) and that every solution of the equation ** 4 = 0 is of class ...
Prove that the o - essential spectrum of the operator t in L , ( I ) is the empty set . E8 ( Bellman ) Suppose that every solution of the equation tf = 0 is of class L , ( 1 ) and that every solution of the equation ** 4 = 0 is of class ...
Page 1557
Prove that the point 2 belongs to the essential spectrum of t . G20 ( Wintner ) . Suppose that q is bounded below , and suppose that 2 does not belong to the essential spectrum of t . Let f be a square - integrable solution of the ...
Prove that the point 2 belongs to the essential spectrum of t . G20 ( Wintner ) . Suppose that q is bounded below , and suppose that 2 does not belong to the essential spectrum of t . Let f be a square - integrable solution of the ...
Page 1568
Prove that a self adjoint extension of the operator has a negative eigenvalue only if 60 ° telg ( t ) | dt 21 . H13 Suppose that Soo ( 1 + t ) g ( t ) \ dt < c . Prove that the origin lies in the continuous spectrum of every self ...
Prove that a self adjoint extension of the operator has a negative eigenvalue only if 60 ° telg ( t ) | dt 21 . H13 Suppose that Soo ( 1 + t ) g ( t ) \ dt < c . Prove that the origin lies in the continuous spectrum of every self ...
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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