Remarks on some limits appearing in the theory of almost periodic functions
Keywords
Almost periodic functions, asymptotic behavior of functions, algebraic numbers, transcendental numbers, Pell's equation, quinary systemAbstract
In this note we are going to present new short proofs concerning either the existence or the non-existence of some limits appearing in the theory of almost periodic functions. Our proofs are completely different from those presented in the papers \cite{DBAN} and \cite{AN}.References
D. Bugajewski and A. Nawrocki, Some remarks on almost periodic functions in view of the Lebesgue measure with applications to linear differential equations, Ann. Acad. Sci. Fenn. Math. 42 (2017), 809–836.
G. M. Hardy and E. M. Wright, An Introduction to the Number Theory, 4th ed., Clarendon Press, 1971.
A. Nawrocki, Diophantine approximations and almost periodic functions, Demonstr. Math. 50 (2017), 100–104.
A. Nawrocki, On some applications of convolution to linear differential equations with Levitan almost periodic coefficients, Topol. Methods Nonlinear Anal. 50 (2017), no. 2, 489–512
A. Nawrocki, On Some Generalizations of Almost Periodic Functions and Their Applications, Ph.D. thesis, AMU in Poznań, 2017 (unpublished, in Polish).
S. Stoiński, Almost Periodic Functions, Scientific Publisher AMU, Poznań, 2008 (in Polish).
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