Related papers: A primer on Fourier Series
This survey article (which will appear as a chapter in the book ``Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions'', Springer-Verlag) provides a small collection of basic material on multiple…
We present some elementary derivations of summation and transformation formulas for q-series, which are different from, and in several cases simpler or shorter than, those presented in the Gasper and Bahman [1990] "Basic Hypergeometric…
These brief lecture notes are intended mainly for undergraduate students in engineering or physics or mathematics who have met or will soon be meeting the Dirac delta function and some other objects related to it. These students might have…
The aim of this review, based on a series of four lectures held at the 22nd "Saalburg" Summer School (2016), is to cover selected topics in the theory of perturbation series and their summation. The first part is devoted to strategies for…
Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
Preliminary version of a book on univariate real analysis, with 14 chapters and 2 appendices. 1. Real numbers; 2. Limits of real sequences; 3. Series; 4. Limits of real functions. 5. Elementary functions; 6. Continuous functions; 7.…
This graduate textbook on machine learning tells a story of how patterns in data support predictions and consequential actions. Starting with the foundations of decision making, we cover representation, optimization, and generalization as…
This paper is the first of a series of introductory papers on the fascinating world of Soergel bimodules. It is combinatorial in nature and should be accessible to a broad audience. The objective of this paper is to help the reader feel…
Basic properties of Fourier integral operators on the torus are studied by using the global representations by Fourier series instead of local representations. The results can be applied to weakly hyperbolic partial differential equations.
In this paper we obtain new sufficient conditions for representation of a function as an absolutely convergent Fourier integral. Unlike those known earlier, these conditions are given in terms of belonging to weighted spaces. Adding weights…
We give a transform of convergent trigonometric series into equivalent convergent series and sufficient conditions for the transformed series to converge faster than the original one.
A q-type Holder condition on a function f is given in order to establish (uniform) convergence of the corresponding basic Fourier series S_q[f] to the function itself, on the set of points of the q-linear grid. Furthermore, by adding others…
We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…
This paper aims to provide a careful and self-contained introduction to the theory of topological degree in Euclidean spaces. It is intended for people mostly interested in analysis and, in general, a heavy background in algebraic or…
This is a textbook about elementary number theory, with emphasis on classical topics around the Euklidean Algorithm.
This book has seven chapters. In chapter one we give the basics needed to make this book a self contained one. Chapter two introduces the notion of interval semigroups and interval semifields and are algebraically analysed. Chapter three…
This is the translation of Euler's Latin textbook Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum (second volume) into English.
We provide an algorithm for computing semi-Fourier sequences for expressions constructed from arithmetic operations, exponentiations and integrations. The semi-Fourier sequence is a relaxed version of Fourier sequence for polynomials…
It is shown that quasi all continuous functions on the unit circle have the property that, for many small subsets E of the circle, the partial sums of their Fourier series considered as functions restricted to E exhibit certain universality…