# periodic function

(redirected from Periodic functions)
Also found in: Encyclopedia.

## periodic function

(ˌpɪərɪˈɒdɪk)
n
(Mathematics) maths a function, such as sin x, whose value is repeated at constant intervals
References in periodicals archive ?
From the solvability conditions for this equation in the class 2[pi]/[sigma] of periodic functions, we obtain the following equality
When we were learning about periodic functions the idea of an essay on periods came to mind.
where [lambda] [member of] C and [p.sub.1](*) and [p.sub.2](*) are real-valued smooth periodic functions with period a.
We argue by contradiction and suppose that there exists a sequence {[u.sub.n]} of periodic functions with period 2[pi] and a corresponding sequence {[t.sub.n]} in (0,1) such that [u.sub.n] is a solution to (17) with [mathematical expression not reproducible] for all n [member of] N, we have a bounded sequence {[P.sub.k][v.sub.n]} in [H.sup.1] (0,2[pi]).For simplicity, we may assume that [v.sub.n] converges to v in [H.sup.1] (0,2[pi]) for some v [member of] N(L) with [mathematical expression not reproducible].
Almost periodic functions, which are an important generalization of periodic functions, were introduced into the field of mathematics by Bohr [1, 2].
The most known periodic functions are trigonometric function, such as sine function.
showed sufficient conditions to ensure the existence and uniqueness of mild solution for (2) in the following classes of vector-valued function spaces: periodic functions, asymptotically periodic functions, pseudo periodic functions, almost periodic functions, asymptotically almost periodic functions, pseudo almost periodic functions, almost automorphic functions, asymptotically almost automorphic functions, pseudo almost automorphic functions, compact almost automorphic functions, asymptotically compact almost automorphic functions, pseudo compact almost automorphic functions, S-asymptotically [omega]-periodic functions, decay functions, and mean decay functions.
Assume that [beta](t) = a + b cos(4t), [gamma](t) = [[gamma].sub.0], a, b, [[gamma].sub.0] [member of] R, b [not equal to] 0 and [alpha](t), [chi](t) are [C.sup.2] periodic functions with the same period [pi].
Taguchi, "Fourier coefficients of periodic functions of Gevrey classes and ultradistributions," Yokohama Mathematical Journal, vol.
O., Best approximations of periodic functions in generalized Lebesgue spaces, Ukrain.
To achieve an analogous goal for a broad family of periodic functions [p.sub.0], we should look at Theorem 3.2.
where the parameter functions A(t), d(t), [[beta].sub.i](t), [[a.sub.i](t), [r.sub.i](t), [[alpha].sub.i](t), [[sigma].sub.i](t) (i = 1,2) are positive, nonconstant, and continuous periodic functions with positive period T.

Site: Follow: Share:
Open / Close