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101.
Edgardo Alvarez Samuel Castillo Manuel Pinto 《Mathematical Methods in the Applied Sciences》2020,43(1):305-319
In this paper, we study a new class of functions, which we call (ω,c)-asymptotically periodic functions. This collection includes asymptotically periodic, asymptotically antiperiodic, asymptotically Bloch-periodic, and unbounded functions. We prove that the set conformed by these functions is a Banach space with a suitable norm. Furthermore, we show several properties of this class of functions as the convolution invariance. We present some examples and a composition result. As an application, we prove the existence and uniqueness of (ω,c)-asymptotically periodic mild solutions to the first-order abstract Cauchy problem on the real line. Also, we establish some sufficient conditions for the existence of positive (ω,c)-asymptotically periodic solutions to the Lasota-Wazewska equation with unbounded oscillating production of red cells. 相似文献
102.
103.
Jean Louis Woukeng 《Mathematical Methods in the Applied Sciences》2014,37(18):2872-2888
In most of the linear homogenization problems involving convolution terms so far studied, the main tool used to derive the homogenized problem is the Laplace transform. Here we propose a direct approach enabling one to tackle both linear and nonlinear homogenization problems that involve convolution sequences without using Laplace transform. To illustrate this, we investigate in this paper the asymptotic behavior of the solutions of a Stokes–Volterra problem with rapidly oscillating coefficients describing the viscoelastic fluid flow in a fixed domain. Under the almost periodicity assumption on the coefficients of the problem, we prove that the sequence of solutions of our ?‐problem converges in L2 to a solution of a rather classical Stokes system. One important fact is that the memory disappears in the limit. To achieve our goal, we use some very recent results about the sigma‐convergence of convolution sequences. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
104.
105.
We define a generalization of the divisor function kin terms of regular convolutions of Narkiewicz and we establish an asymptotic formula for its summatory function in case of cross-convolutions investigated in the first two parts of the present paper. 相似文献
106.
The non-commutative neutrix convolution product of the functions x
r cos–(x) and x
s cos+(x) is evaluated. Further similar non-commutative neutrix convolution products are evaluated and deduced. 相似文献
107.
Franz Lehner 《Proceedings of the American Mathematical Society》1997,125(11):3423-3431
Let be a discrete group and denote by its left regular representation on . Denote further by the free group on generators and its left regular representation. In this paper we show that a subset of has the Leinert property if and only if for some real positive coefficients the identity
holds. Using the same method we obtain some metric estimates about abstract unitaries satisfying the similar identity
108.
V. V. Arestov 《Mathematical Notes》1998,64(3):279-294
We study the relationship between several extremum problems for unbounded linear operators of convolution type in the spaces
, m ≥ 1, 1 ≤ γ ≤ ∞. For the problem of calculating the modulus of continuity of the convolution operatorA on the function classQ defined by a similar operator and for the Stechkin problem on the best approximation of the operatorA on the classQ by bounded linear operators, we construct dual problems in dual spaces, which are the problems on, respectively, the best
and the worst approximation to a class of functions by another class.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 323–340, September, 1998.
This research was supported by INTAS under grant No. 94-4070. 相似文献
109.
Károly J. BöröczkyJr Lars Michael Hoffmann Daniel Hug 《Periodica Mathematica Hungarica》2008,57(2):143-164
Let K be a convex body in ℝ
d
, let j ∈ {1, …, d−1}, and let K(n) be the convex hull of n points chosen randomly, independently and uniformly from K. If ∂K is C
+2, then an asymptotic formula is known due to M. Reitzner (and due to I. Bárány if ∂K is C
+3) for the difference of the jth intrinsic volume of K and the expectation of the jth intrinsic volume of K(n). We extend this formula to the case when the only condition on K is that a ball rolls freely inside K.
Funded by the Marie-Curie Research Training Network “Phenomena in High-Dimensions” (MRTN-CT-2004-511953). 相似文献
110.
A. F. Voronin 《Siberian Mathematical Journal》2008,49(4):601-611
We derive some necessary and sufficient conditions for the well-posedness of a convolution equation of the second kind with even kernel on a finite interval. In order to check these conditions it suffices to compute a one-dimensional integral (of a given function) with precision less than 0.5. As an intermediate result we give a strengthening of the Fredholm alternative for the equation in question with an arbitrary kernel in L 1. 相似文献