Linear Operators: Spectral theory |
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Page 1087
... suppose in addition that the number 2 is in I and that T2 is Hermitian . Show that o ( T2 ) Co ( T , ) for every p in I. 2 54 Let the hypotheses of Exercise 50 be satisfied , and suppose in addition that ( S , E , μ ) is finite . Let p ...
... suppose in addition that the number 2 is in I and that T2 is Hermitian . Show that o ( T2 ) Co ( T , ) for every p in I. 2 54 Let the hypotheses of Exercise 50 be satisfied , and suppose in addition that ( S , E , μ ) is finite . Let p ...
Page 1144
... Suppose that each of the s regions into which the plane is divided by these arcs is contained in an angular sector of opening less than л / p . Let N > 0 be an integer , and suppose that the resolvent of T satisfies the inequality | R ...
... Suppose that each of the s regions into which the plane is divided by these arcs is contained in an angular sector of opening less than л / p . Let N > 0 be an integer , and suppose that the resolvent of T satisfies the inequality | R ...
Page 1602
... suppose that the equation ( 2–7 ) ƒ linearly independent solutions ƒ and g such that S ' ' \ ƒ ' ( s ) [ 2 ds = O ( t2 ) and [ ' " ' \ g ' ( s ) \ 2 ds = O ( t2 ) . Then the point λ belongs to the essential spectrum of 7 ( Hartman and ...
... suppose that the equation ( 2–7 ) ƒ linearly independent solutions ƒ and g such that S ' ' \ ƒ ' ( s ) [ 2 ds = O ( t2 ) and [ ' " ' \ g ' ( s ) \ 2 ds = O ( t2 ) . Then the point λ belongs to the essential spectrum of 7 ( Hartman and ...
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