On a generalized Volterra equation in Hilbert space
HTML articles powered by AMS MathViewer
- by Romano M. De Santis
- Proc. Amer. Math. Soc. 38 (1973), 563-570
- DOI: https://doi.org/10.1090/S0002-9939-1973-0317102-4
- PDF | Request permission
Abstract:
The objective of this paper is to establish a fundamental theorem on the existence and uniqueness of the solution of a generalized Volterra equation in Hilbert space. Some applications to the areas of abstract functional analysis and modern mathematical systems theory are pointed out.References
- M. S. Brodskiĭ, On the triangular representation of completely continuous operators with one-point spectra, Uspehi Mat. Nauk 16 (1961), no. 1 (97), 135–141 (Russian). MR 0130566 M. Damborg and A. Naylor, The fundamental structure of input-output stability for feedback systems, IEEE Trans. on System Science and Cybernetics, April, 1970. R. M. De Santis, Causality structure of engineering systems, Ph.D. Thesis, University of Michigan, Ann Arbor, Mich., 1971. —, Causality, strict causality and invertibility for systems in Hilbert resolution spaces, Technical Report DA-AN-72-006, École Polytechnique, Montréal, Canada.
- I. C. Gohberg and M. G. Kreĭn, Theory and applications of Volterra operators in Hilbert space, Translations of Mathematical Monographs, Vol. 24, American Mathematical Society, Providence, R.I., 1970. Translated from the Russian by A. Feinstein. MR 0264447
- R. Saeks, Causality in Hilbert space, SIAM Rev. 12 (1970), 357–383. MR 412893, DOI 10.1137/1012080
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 563-570
- MSC: Primary 47B99; Secondary 45D05, 47A60
- DOI: https://doi.org/10.1090/S0002-9939-1973-0317102-4
- MathSciNet review: 0317102