Abstract
The Bohr compactification is shown to be the natural setting for studying almost periodic functions. Applications to partial differential equations are also given.
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Amerio, L. andProuse, G., Almost Periodic Functions and Functional Equations, Van Nostrand, 1971.
Avantaggiati, A., Bruno, G. andIannacci, R.,Classical and new results on Besicovitch spaces of almost periodic functions and their duals, Quad. Dip. Met. Mod. Mat., Univ. di Roma “La Sapienza”, 1993.
Avantaggiati, A., Bruno, G. andIannacci, R.,The Hausdorff-Young theorem for almost periodic functions and some applications, Nonlinear. Analysis, Theory, Meth. Appl,25 (1995), 61–87.
Besicovitch, A., Almost Periodic Functions, Dover, New York, 1954.
Fournier, G., Szulkin, A. andWillem, M.,Almost periodic solutions of elliptic equations on R N, Preprint, Inst. Math. Pure Appl., Univ. Cathol. Louvain, 1993 (to be published in SIAM J. Math. Anal.).
Hewitt, E. andRoss, K., Abstract Harmonic Analysis, Springer, 1979.
Levitan, B.M. andZhikov, V.V., Almost Periodic Functions and Differential Equations, Cambridge Univ. Press, 1982.
Mukhamadiev, E.,On invertibility of partial difference operators of elliptic type, Dokl. Akad. Nauk SSSR,205 no 6 (1972), 1292–1295, (in Russian).
Pankov, A.,On nonlinear second order elliptic equations with almost periodic coefficients, Ukr. Mat. Zh,35 no 5 (1983), 649–652, (in Russian).
Pankov, A., Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equations, Kluwer, Dordrecht, 1990.
Schmitt, K. andWard, J.R. Jr.,Almost periodic solutions of nonlinear second order differential equations, Results Math,21 (1992), 190–199.
Schmitt, K. andWard, J.R. Jr.,Periodic and almost periodic solutions of nonlinear evolution equations, Preprint.
Shubin, M.A.,Almost periodic functions and differential equations, Uspekhi Mat. Nauk,33 no 2 (1978), 3–47, (in Russian).
Ward, J.R. Jr.,Bounded and almost periodic solutions of semilinear parabolic equations, Rocky Mountain J. Math,18 (1988).
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Conferenza tenuta il 20 maggio 1996
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Pankov, A. Almost periodic functions, Bohr compactification, and differential equations. Seminario Mat. e. Fis. di Milano 66, 149–158 (1996). https://doi.org/10.1007/BF02925358
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DOI: https://doi.org/10.1007/BF02925358