Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |
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Page 2029
RN Similarly , functions on RN may determine tempered distributions just as they
sometimes determine distributions . For example , since convergence on → in 0
is equivalent to the statement that for any two polynomials P , Q in N variables ...
RN Similarly , functions on RN may determine tempered distributions just as they
sometimes determine distributions . For example , since convergence on → in 0
is equivalent to the statement that for any two polynomials P , Q in N variables ...
Page 2054
... and ( ii ) ( iii ) T ( 1 ) H ? 5 ( 2 ) T ( 2 ) ( RN ) , t > 0 . For every qo ) in H2 there is
a uniquely determined continuous map t o ( t ) of ( 0 , 0 ) into H2 ( of ( - 00 , 0 ] into
H2 if a ? < 0 ) which is differentiable for t > 0 and has the properties olt ) e ( 2 ) T ...
... and ( ii ) ( iii ) T ( 1 ) H ? 5 ( 2 ) T ( 2 ) ( RN ) , t > 0 . For every qo ) in H2 there is
a uniquely determined continuous map t o ( t ) of ( 0 , 0 ) into H2 ( of ( - 00 , 0 ] into
H2 if a ? < 0 ) which is differentiable for t > 0 and has the properties olt ) e ( 2 ) T ...
Page 2373
which exclude the whole complex plane from the spectrum of the operator they
determine . ... These boundary conditions determine discrete differential
operators having eigenvalues 1 = determined by equations of the form sin 8 = ks .
which exclude the whole complex plane from the spectrum of the operator they
determine . ... These boundary conditions determine discrete differential
operators having eigenvalues 1 = determined by equations of the form sin 8 = ks .
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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 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 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
Bibliographic information
| Title | Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 Volume 7 of Pure and applied mathematics |
| Authors | Nelson Dunford, Jacob Theodore Schwartz |
| Publisher | Wiley Interscience, 1963 |
| Original from | the University of Michigan |
| Digitized | 2 Feb 2010 |
| ISBN | 0471226394, 9780471226390 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |