Linear Operators, Part 2 |
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Page 1917
... self adjointness . The ana- lytical details necessary for the application of this method of Friedrichs are , in fact ... adjoint , then a non - rigorous formal argument can be used to buttress the expectation that the Friedrichs operator U ...
... self adjointness . The ana- lytical details necessary for the application of this method of Friedrichs are , in fact ... adjoint , then a non - rigorous formal argument can be used to buttress the expectation that the Friedrichs operator U ...
Page 2017
... example , consider the formal differential operator G ( 14 ) 2 %%% -ai Əs2 22 Bi as2 where a , ẞ are positive real numbers . If a B , the corresponding closed operator A cannot be self adjoint , but it always has a resolution of the ...
... example , consider the formal differential operator G ( 14 ) 2 %%% -ai Əs2 22 Bi as2 where a , ẞ are positive real numbers . If a B , the corresponding closed operator A cannot be self adjoint , but it always has a resolution of the ...
Page 2305
... formal differential operator d ( 1 -t2 ) dt - d 2x2 282 + + dt 1 + t 1 - t of the first part of Section XIII.8 , and again make ... formal differential operator defines a unique self adjoint operator L in the Hilbert space L2 ( −1 , +1 ) ...
... formal differential operator d ( 1 -t2 ) dt - d 2x2 282 + + dt 1 + t 1 - t of the first part of Section XIII.8 , and again make ... formal differential operator defines a unique self adjoint operator L in the Hilbert space L2 ( −1 , +1 ) ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero