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On the preservation of periodic monotonicity

Authors:

Institution:

1. Mathematisches Institut, Universit?t Würzburg, W-8700, Würzburg, Germany
2. Departmento de Matemática, Universidad Técnica F. Santa María, Valparaíso, Chile

Abstract:

A 2

-periodic continuous real functionf is said to beperiodically monotone if it has the following property: there exist numbert ₁

t ₂

t ₃

t ₁+2

such thatf is nonincreasing fort ₁

t ₂ and nondecreasing int ₂

t ₃. For any 2 pgr

-periodic, integrable real functiong with int

₀ ² |g(t|dt infin

) we define

$(f * g)(x): = \frac{1}{{2\pi }}\int_0^{2\pi } {f(t)} g(x - t)dt$

Keywords:	AMS classification" target="_blank">AMS classification 42A45 42A85
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