## Linear Operators: Spectral operators |

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Page 2548

Transformations of Fourier and Laplace types of means of solutions of differential

equations of second order . Doklady Akad . Nauk SSSR 106 , 187 – 190 ( 1956 ) .

(

Transformations of Fourier and Laplace types of means of solutions of differential

equations of second order . Doklady Akad . Nauk SSSR 106 , 187 – 190 ( 1956 ) .

(

**Russian**) Math . Rev . 18 , 35 ( 1957 ) . Leżański , T . 1 . The Fredholm theory ...Page 2549

(

functions of a non - selfadjoint differential operator with spectral singularities .

Doklady Akad . Nauk SSSR 149 , 256 – 259 ( 1963 ) . (

Dokl .

(

**Russian**) Math . Rev . 33 # 4680 , 792 ( 1967 ) . 6 . Expansion in characteristicfunctions of a non - selfadjoint differential operator with spectral singularities .

Doklady Akad . Nauk SSSR 149 , 256 – 259 ( 1963 ) . (

**Russian**) Soviet Math .Dokl .

Page 2552

The root - vector expansion of a weakly perturbed self - adjoint operator . Doklady

Akad . Nauk SSSR 142 , 538 – 541 ( 1962 ) . (

361 ( 1964 ) . Eigenvalues and singular values of the sum and product of linear ...

The root - vector expansion of a weakly perturbed self - adjoint operator . Doklady

Akad . Nauk SSSR 142 , 538 – 541 ( 1962 ) . (

**Russian**) Math . Rev . 27 # 1837 ,361 ( 1964 ) . Eigenvalues and singular values of the sum and product of linear ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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### Common terms and phrases

adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero