Infinite-Dimensional Systems: Proceedings of the Conference on Operator Semigroups and Applications Held in Retzhof (Styria), Austria, June 5-11, 1983F. Kappel, W. Schappacher |
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Page 55
... Moreover J ( E ) is dense in F , since ( f , g ) ~ = Flim J ( xn ) ( 2.6 ) where n + ∞ X = g n nAR ( n , A ) f and R ( n , A ) is the resolvent of A. ( 2.7 ) Remark also that , due to ( 2.5 ) and the closed graph theorem , F is ...
... Moreover J ( E ) is dense in F , since ( f , g ) ~ = Flim J ( xn ) ( 2.6 ) where n + ∞ X = g n nAR ( n , A ) f and R ( n , A ) is the resolvent of A. ( 2.7 ) Remark also that , due to ( 2.5 ) and the closed graph theorem , F is ...
Page 80
... moreover 0 € p ( Â ) and fractional powers ~ Y A of A may be defined and we can introduce the interpolation spaces with norm X = Henceforth Y = 1/2 . We define a family of nonlinear operators { Ĵ ( t ) | t e [ 0 , T ] } by 2 P ( t ) ...
... moreover 0 € p ( Â ) and fractional powers ~ Y A of A may be defined and we can introduce the interpolation spaces with norm X = Henceforth Y = 1/2 . We define a family of nonlinear operators { Ĵ ( t ) | t e [ 0 , T ] } by 2 P ( t ) ...
Page 198
... Moreover , the optimal cost is given by J ( u ) = < , π > π 2 M Με ( 39 ) ( b ) If ( 35 ) is satisfied , then there exists at most one non - negative self adjoint solution e L ( M2 ) of ( 38 ) . Moreover if π is such a solution , the ...
... Moreover , the optimal cost is given by J ( u ) = < , π > π 2 M Με ( 39 ) ( b ) If ( 35 ) is satisfied , then there exists at most one non - negative self adjoint solution e L ( M2 ) of ( 38 ) . Moreover if π is such a solution , the ...
Contents
st of Part teipants | 1 |
Axles and 2 A Goldstein | 16 |
S N Busenberg | 23 |
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adjoint Anal analytic assume asymptotic behavior Au(t Banach space bounded compact consider constant defined delay differential equations denote Dirichlet eigenfunction elliptic operators equivalent estimate evolution equations exists feedback finite forcing function semigroup functional differential equations given hence Hilbert space holds hypothesis implies inequality infinite delay initial function semigroup integral equations Invertibility Condition 2.8 Lemma linear operators Math Moreover nonlinear norm obtain partial differential equations perturbation positive semigroup proof of Theorem prove rate of convergence resolvent Riccati equation s.c. semigroup satisfies Section selfadjoint semigroup S(t sequence spectral strongly continuous strongly continuous semigroup subset subspace t₁ Theorem 2.1 theory u e D(A uniformly unique solution vectors Volterra equations Volterra integral equations zero ε ε ик