Almost Periodic Solutions for Some Convolution Equations

Corduneanu, Silvia-Otilia

doi:10.2478/auom-2013-0044

Abstract

We use the theory of Fourier series for almost periodic functions to looking for complex-valued functions f which are almost periodic on R and satisfy the following equation

In this context g and h are almost periodic functions on ℝ and ϕ belongs to L¹(ℝ).

References

[1] Ait Dads, E., Ezzinbi, K.: Existence of positive pseudo almost periodic solution for a class of functional equations arising in epidemic problems, Cybernet. Systems Anal., 30 (1994), No. 6 , 900-910.
Search in Google Scholar
[2] Ait Dads, E., Cieutat, P., Lhachimi, L.: Existence of positive almost periodic or ergodic solutions for some neutral nonlinear integral equations, Differential and Integral Equations, 22 (2009), No. 11-12, 1075-1096.
Search in Google Scholar
[3] Argabright, L.N., Gil de Lamadrid, J.: Fourier Analysis of Unbounded Measures on Locally Compact Abelian Groups, Mem. Amer. Math. Soc. 145 (1974).10.1090/memo/0145
Search in Google Scholar
[4] Argabright, L.N., Gil de Lamadrid, J: Almost Periodic Measures, Mem. Amer. Math. Soc. 428 (1990).10.1090/memo/0428
Search in Google Scholar
[5] Corduneanu, C.: Almost Periodic Functions, Interscience Publishers, New York, London, Sydney, Toronto, 1968.
Search in Google Scholar
[6] Corduneanu, S.O.: Inequalities for Almost Periodic Measures, Mathematical Inequalities & Applications, Volume 5, No. 1 (2002), 105 - 111.
Search in Google Scholar
[7] Corduneanu, S.O.: Inequalities for a Class of Means with Parameter, Buletinul Institutului Politehnic din Iasi, Tomul LIII (LVII), Fasc. 5, 2007, 77-84.
Search in Google Scholar
[8] Corduneanu, S.O.: Equations Involving the Mean of Almost Periodic Measures, Operator Theory: Advances and Applications, 201 (2009), Birkhuser Verlag Basel/Switzerland, 125-133.
Search in Google Scholar
[9] Corduneanu, S.O.: Positive Almost Periodic Solutions of Some Convolution Equations, Positivity 14 (2010), DOI 10.1007/s11117-010-0081-9, 623-636.
Search in Google Scholar
[10] Deimling, K.: Nonlinear analysis, Springer-Verlag, Berlin, 1985.
Search in Google Scholar
[11] Eberlein, W.F.: Abstract Ergodic Theorems and Weak Almost Periodic Functions, Trans Amer. Math. Soc. 67(1949), 217-240.10.1090/S0002-9947-1949-0036455-9
Search in Google Scholar
[12] Ezzinbi, K., Hachimi, M.A.: Existence of positive almost periodic solutions of functional equations via Hilbert's projective metric, Nonlinear Anal., 26 (1996), 1169-1176.10.1016/0362-546X(94)00331-B
Search in Google Scholar
[13] Gil de Lamadrid, J.: Sur les Mesures Presque Périodiques, Asterisque 4, 1973, 61-89.
Search in Google Scholar
[14] Hewitt, E., Ross, K.A.: Abstract Harmonic Analysis Vol. I, Springer - Verlag, Berlin, Gottingen, Heidelberg, 196310.1007/978-3-662-40409-6
Search in Google Scholar
[15] Rudin, W.: Fourier Analysis on Groups, Interscience Tracts in Pure and Applied Mathematics, Number 12, Interscience Publishers - John Wiley and Sons, New York, London, 1962.
Search in Google Scholar

Almost Periodic Solutions for Some Convolution Equations

Abstract

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