相关论文: On Fubini type theorems for the Riemann integral

Reciprocal transformations mix the role of the dependent and independent variables of (nonlinear partial) differential equations to achieve simpler versions or even linearized versions of them. These transformations help in the…

We introduce a symbolic method for the evaluation of definite integrals containing combinations of various functions, including exponentials, logarithm and products of Bessel functions of different types. The method we develop is naturally…

We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained…

A well-known result by Larson and Sweedler shows that integrals on a Hopf algebra can be obtained by applying the Structure Theorem for Hopf modules to the rational part of its linear dual. This fact can be rephrased by saying that taking…

Runge's method is a tool to figure out integral points on curves effectively in terms of height. This method has been generalised to varieties of any dimension, unfortunately its conditions of application are often too restrictive. In this…

In this paper I give an evaluation of a functional integral by means of a series in functional derivatives, first of all we propose a differential equation of first order and solve it by iterative methods, to obtain a series for the…

Integration by parts identities (IBPs) can be used to express large numbers of apparently different d-dimensional Feynman Integrals in terms of a small subset of so-called master integrals (MIs). Using the IBPs one can moreover show that…

Gauge-fixed correlation functions are a valuable tool in intermediate steps when determining gauge-invariant physics. However, when obtaining them in different calculations, it is necessary to use exactly the same definition of the gauge to…

The reconstruction theorem and the multilevel Schauder estimate have central roles in the analytic theory of regularity structures [17]. Inspired by [26], we provide elementary proofs for them by using the semigroup of operators.…

In this talk we discuss the interplay of two elliptic curves, which occur in different sub-sectors of Feynman integrals. We analyse a particular Feynman integral depending on two elliptic curves and derive an associated differential…

The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a…

We introduce a general definition of hybrid transforms for constructible functions. These are integral transforms combining Lebesgue integration and Euler calculus. Lebesgue integration gives access to well-studied kernels and to regularity…

The paper presents a survey over frame multipliers and related concepts. In particular, it includes a short motivation of why multipliers are of interest to consider, a review as well as extension of recent results, devoted to the…

We further develop the \emph{Multivariate Decomposition Method} (MDM) for the Lebesgue integration of functions of infinitely many variables $x_1,x_2,x_3,\ldots$ with respect to a corresponding product of a one dimensional probability…

Canonical Feynman integrals are of great interest in the study of scattering amplitudes at the multi-loop level. We propose to construct $d\log$-form integrals of the hypergeometric type, treat them as a representation of Feynman integrals,…

We consider nonlinear, or "event-dependent", sampling, i.e. such that the sampling instances {tk} depend on the function being sampled. The use of such sampling in the construction of Lebesgue's integral sums is noted and discussed as…

By a theorem due to the first author, the bounded derived category of a finite-dimensional algebra over a field embeds fully faithfully into the stable category over its repetitive algebra. This embedding is an equivalence iff the algebra…

Complex analysis is a powerful tool to study classical integrable systems, statistical physics on the random lattice, random matrix theory, topological string theory,... All these topics share certain relations, called "loop equations" or…

The study of the pentagon (fusion) equation leds to the Structure and the Classification theorem for finite dimenasional Hopf algebras: there exists a one to one correspondence between the set of types of n-dimensional Hopf algebtras and…

When introduced in a 2018 article in the American Mathematical Monthly, the omega integral was shown to be an extension of the Riemann integral. Although results for continuous functions such as the Fundamental Theorem of Calculus follow…