## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2493

Suppose also that A and B are integral operators with Hölder - continuous

three ...

Suppose also that A and B are integral operators with Hölder - continuous

**kernels**a ( x , y ) and B ( x , y ) . Then BR ( A ) A is the integral operator with the**kernel**po b ( x , t ) alt , y ) 14 . dt ; da at this**kernel**is Hölder - continuous in all thethree ...

Page 2499

... →æf ( x ) in a space of vector valued functions , in which H2 = H + V where V is

an integral operator with a smooth

similarity method of Section 2 is assumed to apply . Then , as shown in Section 2

...

... →æf ( x ) in a space of vector valued functions , in which H2 = H + V where V is

an integral operator with a smooth

**kernel**V ( x , y ) , and in which the Friedrichssimilarity method of Section 2 is assumed to apply . Then , as shown in Section 2

...

Page 2502

Krein proves that the function log 4 ( z ) has the integral representation log 4 ( z )

= ptoo dia ) J - a iz where the

( A ) | dd S | | H - Hill , the norm on the right being the trace norm of Chapter XI .

Krein proves that the function log 4 ( z ) has the integral representation log 4 ( z )

= ptoo dia ) J - a iz where the

**kernel**function 8 satisfies the integral inequality 518( A ) | dd S | | H - Hill , the norm on the right being the trace norm of Chapter XI .

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator 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 positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero