An inequality for positive definite Volterra kernels
Author:
Olof J. Staffans
Journal:
Proc. Amer. Math. Soc. 58 (1976), 205210
MSC:
Primary 45M05; Secondary 45D05
MathSciNet review:
0500049
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Abstract: We deduce an inequality satisfied by certain positive definite Volterra kernels. This inequality yields a new theorem on the asymptotic behavior of the bounded solutions of a Volterra equation.
 [1]
A.
Halanay, On the asymptotic behavior of the solutions of an
integrodifferential equation, J. Math. Anal. Appl 10
(1965), 319–324. MR 0176304
(31 #579)
 [2]
StigOlof
Londen, On a nonlinear Volterra integral equation, J.
Differential Equations 14 (1973), 106–120. MR 0340995
(49 #5745)
 [3]
StigOlof
Londen, On the variation of the solutions of a nonlinear integral
equation, J. Math. Anal. Appl. 52 (1975), no. 3,
430–449. MR 0420177
(54 #8192)
 [4]
, On an integral equation in a Hilbert space, Univ. of Wisconsin, MRC Technical Summary Report 1527, 1975.
 [5]
R.
C. MacCamy and J.
S. W. Wong, Stability theorems for some functional
equations, Trans. Amer. Math. Soc. 164 (1972), 1–37. MR 0293355
(45 #2432), http://dx.doi.org/10.1090/S0002994719720293355X
 [6]
J.
A. Nohel and D.
F. Shea, Frequency domain methods for Volterra equations,
Advances in Math. 22 (1976), no. 3, 278–304. MR 0500024
(58 #17748)
 [7]
Olof
J. Staffans, Nonlinear Volterra integral equations
with positive definite kernels, Proc. Amer.
Math. Soc. 51
(1975), 103–108. MR 0370081
(51 #6310), http://dx.doi.org/10.1090/S00029939197503700818
 [8]
Olof
J. Staffans, Positive definite measures with
applications to a Volterra equation, Trans.
Amer. Math. Soc. 218 (1976), 219–237. MR 0458086
(56 #16289), http://dx.doi.org/10.1090/S00029947197604580865
 [9]
Olof
J. Staffans, Tauberian theorems for a positive
definite form, with applications to a Volterra equation, Trans. Amer. Math. Soc. 218 (1976), 239–259. MR 0422936
(54 #10921), http://dx.doi.org/10.1090/S00029947197604229369
 [10]
Olof
J. Staffans, On the asymptotic spectra of the bounded solutions of
a nonlinear Volterra equation, J. Differential Equations
24 (1977), no. 3, 365–382. MR 0463855
(57 #3794)
 [1]
 A. Halanay, On the asymptotic behavior of the solutions of an integrodifferential equation, J. Math. Anal. Appl. 10 (1965), 319324. MR 31 #579. MR 0176304 (31:579)
 [2]
 S.O. Londen, On a nonlinear Volterra integral equation, J. Differential Equations 14 (1973), 106120. MR 49 #5745. MR 0340995 (49:5745)
 [3]
 , On the variation of the solutions of a nonlinear integral equation, J. Math. Anal. Appl. 52 (1975), 430449. MR 0420177 (54:8192)
 [4]
 , On an integral equation in a Hilbert space, Univ. of Wisconsin, MRC Technical Summary Report 1527, 1975.
 [5]
 R. C. MacCamy and J. S. W. Wong, Stability theorems for some functional equations, Trans. Amer. Math. Soc. 164 (1972), 137. MR 45 #2432. MR 0293355 (45:2432)
 [6]
 J. A. Nohel and D. F. Shea, Frequency domain methods for Volterra equations, Advances in Math. (to appear). MR 0500024 (58:17748)
 [7]
 O. J. Staffans, Nonlinear Volterra integral equations with positive definite kernels, Proc. Amer. Math. Soc. 51 (1975), 103108. MR 0370081 (51:6310)
 [8]
 , Positive definite measures with applications to a Volterra equation, Trans. Amer. Math. Soc. 218 (1976), 219237. MR 0458086 (56:16289)
 [9]
 , Tauberian theorems for a positive definite form, with applications to a Volterra equation, Trans. Amer. Math. Soc. 219 (1976), 239259. MR 0422936 (54:10921)
 [10]
 , On the asymptotic spectra of the bounded solutions of a nonlinear Volterra equation, J. Differential Equations (to appear). MR 0463855 (57:3794)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197605000490
PII:
S 00029939(1976)05000490
Article copyright:
© Copyright 1976
American Mathematical Society
