Related papers: A simplified multidimensional integral
Linear functions are arguably the most mundane among all functions. However, the basic fact that a multi-variable linear function has a constant gradient field can provide simple geometric insights into several familiar results such as the…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
A new classification of real functions and other related real objects defined within a compact interval is proposed. The scope of the classification includes normal real functions and distributions in the sense of Schwartz, referred to…
This short note presents a peculiar generalization of the Riemann hypothesis, as the action of the permutation group on the elements of continued fractions. The problem is difficult to attack through traditional analytic techniques, and…
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
A new parametric integral is obtained as a consequence of the Riemann hypothesis. An asymptotic multiplicability is the main property of this integral.
In many articles on the integral expressions of Mittag-Leffler functions, we have found that whether the integral expression can be used at the origin is still unresolved. In this article we give the applicable conditions and proof. And we…
We present a replacement for traditional Riemann integrals in undergraduate calculus, which supplements naive precalculus and at the same time opens a way to more sophisticated theories such as Lebesgue integration.
Derivative of a function can be expressed in terms of integration over a small neighborhood of the point of differentiation, so-called differentiation by integration method. In this text a maximal generalization of existing results which…
In this paper, we give one possible definition for functions of several variables applied to endomorphisms of finite dimensional C-vector spaces. This definition is consistent with the usual notion of a function of a square matrix. Some…
We define a simplicial differential calculus by generalizing divided differences from the case of curves to the case of general maps, defined on general topological vector spaces, or even on modules over a topological ring K. This calculus…
In this paper, we intend to revisit Theorem 2 of [3] formulating it in a way that, weakening the hypotheses and, at the same time, highlighting the richer conclusion allowed by the proof, it can potentially be applicable to a broader range…
Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.
For nice functions, invariant means over integral currents (certain generalized surfaces), can be uniquely defined.
The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…
The paper presents new and known results on estimates of important linear and nonlinear approximation characteristics of generalized Wiener classes of functions of several variables in different metrics.
This work introduces a new inversion formula for analytical functions. It is simple, generally applicable and straightforward to use both in hand calculations and for symbolic machine processing. It is easier to apply than the traditional…
We obtain a new decomposition of the Riemann-Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class $C^n$, $n \in \mathbb{N}$, and allow us to…
We study the complexity of deterministic and probabilistic inversions of partial computable functions on the reals.
Approximating a manifold-valued function from samples of input-output pairs consists of modeling the relationship between an input from a vector space and an output on a Riemannian manifold. We propose a function approximation method that…