41A10Exact values are obtained of the n-widths of 2π-periodic functions of the form $$ f(x)=\\frac{1}{2\\pi} \\int_{0}^{2\\pi}{\\mathcal{K}}(x-t)\\varphi(t){m d}t=({\\mathcal{K}}*\\varphi)(x)$$ f ( x ) = 1 2 π ∫ 0 2 π K ( x t ) φ ( t ...
This course helps to build the foundational material to use mathematics as a tool to model, understand, and interpret the world around us. This is done through studying functions, their properties, and applications to data analysis. Concepts of precalculus provide the set of tools for the beginn...
The purpose of the paper is to discuss methods for constructing weighted cubature formulas in Sobolev spaces with periodic members. These formulas are intended to approximate the calculation of Fourier coefficients of functions under consideration. The explicit formulas for the weights and the errors of...
The theory of almost periodic functions, mainly created during the 1920s by the Danish mathematician H. Bohr (1887–1951), is a powerful tool to study a wide class of trigonometric series of the general type and even exponential series (in this context, we can cite among others the papers ...
J. A. C. Weideman, Numerical integration of periodic functions: a few examples, Amer. Math. Monthly 109 (2002), 21-36. MR1903510 (2003c:65017) Program in Applied Mathematics, The University of Arizona, Tucson, Arizona 85721-J. A. C. WEIDEMAN, Numerical integration of periodic functions...
In the first part of the paper we examine mappings of higher order from a general point of view, that is, in normed spaces of bounded real-valued functions defined on R. Particular attention is paid to the relation of such mappings with the so-called autonomous superposition operators. Next...
There exists a bounded open set \(\Delta \subset C_{\omega }\), the set of all continuous, \(\omega\)-periodic functions: \(\mathbb {R}\rightarrow \mathbb {R}^{n}\), such that for any \(\lambda \in (0,1)\), each \(\omega\)-periodic function x(t) of the inclusion ...
Mathematics 2023, 11, 2042 9 of 10 5. Conclusions In this paper, the joint approximation of a pair of analytic functions by shifts of absolutely convergent Dirichlet series ∑ζnT (s; a) = ∞ m=1 amvnT (m; ms θ) and ζnT (s, α; b) = ∞∑ m=0 bm vnT (m (m, α; + ...
A typical example of a nonlinearity f(x,t) satisfying the hypotheses of Theorem 1.2 isf(x,t):=a(x)t+b(x)|t|p−2t(et−1),x∈R2,t∈R, where a,b are continuous and periodic functions satisfying λ≤a≤|a|≤γ, b≥0 in R2. We quote that there are few existence results ...
Deep learning architectures can provide very expressive models for function approximation, and have proven very effective in numerous contexts1,2,3. Unfortunately, standard non-structure-preserving neural networks struggle to learn the symmetries and conservation laws underlying dynamical systems, and as a...