Evolution system approximations of solutions to closed linear operator equations
Author:
Seaton D. Purdom
Journal:
Trans. Amer. Math. Soc. 215 (1976), 6379
MSC:
Primary 47B44; Secondary 47A50
MathSciNet review:
0420331
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: With S a linearly ordered set with the least upper bound property, with g a nonincreasing realvalued function on S, and with A a densely defined dissipative linear operator, an evolution system M is developed to solve the modified Stieljes integral equation . An affine version of this equation is also considered. Under the hypothesis that the evolution system associated with the linear equation is strongly (resp. weakly) asymptotically convergent, an evolution system is used to approximate strongly (resp. weakly) solutions to the closed operator equation .
 [1]
F.
E. Browder and W.
V. Petryshyn, The solution by iteration of nonlinear
functional equations in Banach spaces, Bull.
Amer. Math. Soc. 72
(1966), 571–575. MR 0190745
(32 #8155b), http://dx.doi.org/10.1090/S000299041966115446
 [2]
Frank
Gilfeather, Asymptotic convergence of operators in
Hilbert space, Proc. Amer. Math. Soc. 22 (1969), 69–76. MR 0247508
(40 #773), http://dx.doi.org/10.1090/S00029939196902475082
 [3]
J.
V. Herod, A pairing of a class of evolution
systems with a class of generators., Trans.
Amer. Math. Soc. 157 (1971), 247–260. MR 0281059
(43 #6778), http://dx.doi.org/10.1090/S00029947197102810598
 [4]
, Generators for evolution systems with quasicontinuous trajectories, Pacific J. Math. (to appear).
 [5]
J.
S. MacNerney, Integral equations and semigroups, Illinois J.
Math. 7 (1963), 148–173. MR 0144179
(26 #1726)
 [6]
J.
S. MacNerney, A linear initialvalue
problem, Bull. Amer. Math. Soc. 69 (1963), 314–329. MR 0146613
(26 #4133), http://dx.doi.org/10.1090/S000299041963109052
 [7]
J.
S. MacNerney, A nonlinear integral operation, Illinois J.
Math. 8 (1964), 621–638. MR 0167815
(29 #5082)
 [8]
Robert
H. Martin Jr., Product integral approximations of
solutions to linear operator equations, Proc.
Amer. Math. Soc. 41
(1973), 506–512. MR 0380463
(52 #1363), http://dx.doi.org/10.1090/S00029939197303804634
 [9]
Kôsaku
Yosida, Functional analysis, Second edition. Die Grundlehren
der mathematischen Wissenschaften, Band 123, SpringerVerlag New York Inc.,
New York, 1968. MR 0239384
(39 #741)
 [1]
 F. E. Browder and W. V. Petryshyn, The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 571575. MR 32 #8155b. MR 0190745 (32:8155b)
 [2]
 F. Gilfeather, Asymptotic convergence of operators in Hilbert space, Proc. Amer. Math. Soc. 22 (1969), 6976. MR 40 #773. MR 0247508 (40:773)
 [3]
 J. V. Herod, A pairing of a class of evolution systems with a class of generators, Trans. Amer. Math. Soc. 157 (1971), 247260. MR 43 #6778. MR 0281059 (43:6778)
 [4]
 , Generators for evolution systems with quasicontinuous trajectories, Pacific J. Math. (to appear).
 [5]
 J. S. MacNerney, Integral equations and semigroups, Illinois J. Math. 7 (1963), 148173. MR 26 #1726. MR 0144179 (26:1726)
 [6]
 , A linear initialvalue problem, Bull. Amer. Math. Soc. 69 (1963), 314329. MR 26 #4133. MR 0146613 (26:4133)
 [7]
 , A nonlinear integral operation, Illinois J. Math. 8 (1964), 621638. MR 29 #5082. MR 0167815 (29:5082)
 [8]
 R. H. Martin, Jr., Product integral approximations of solutions to linear operator equations, Proc. Amer. Math. Soc. 41 (1973), 506512. MR 0380463 (52:1363)
 [9]
 K. Yosida, Functional analysis, 2nd ed., Die Grundlehren der math. Wissenschaften, Band 123, SpringerVerlag, New York, 1968. MR 39 #741. MR 0239384 (39:741)
Similar Articles
Retrieve articles in Transactions of the American Mathematical Society
with MSC:
47B44,
47A50
Retrieve articles in all journals
with MSC:
47B44,
47A50
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002994719760420331X
PII:
S 00029947(1976)0420331X
Keywords:
Dissipative,
evolution system,
product integral,
asymptotically convergent
Article copyright:
© Copyright 1976
American Mathematical Society
