Related papers: A higher-dimensional version of F\'ary's theorem

We prove a uniqueness theorem for an entire function, which shares certain values with its higher order derivatives.

In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.

We formulate an exponential Diophantine equation, which is is some sense one order higher that Fermat's Last Theorem. We also give three examples of solutions to this exponential Diophantine equation and formulate a conjecture.

We revise a proof of a Mazur-Ulam theorem for generalized gyrovector spaces.

The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…

We give a new simpler proof of a theorem of Jayne and Rogers.

The Flavour Expansion Theorem, which has been recently proposed as a more general and elegant algebraic method, for the derivation of the commonly used Mass Insertion Approximation, is revisited. The theorem is reviewed, with respect to its…

We prove the following statement. Let $f\in\mathbb{R}[x_1,\ldots,x_d]$, for some $d\ge 3$, and assume that $f$ depends non-trivially in each of $x_1,\ldots,x_d$. Then one of the following holds. (i) For every finite sets…

We prove finite-field analogs of Bourgain's projection theorem in higher dimensions. In particular, for a certain range of parameters we improve on an exceptional set estimate by Chen in all dimensions and codimensions.

We present a simple dyadic construction that yields a new counterexample to Zygmund's conjecture. Our result recovers Soria's classical result in dimension three, through a different construction, and gives new ones in all other dimensions…

We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.

We prove a four dimensional version of the Bernstein Theorem, with complex polynomials being replaced by quaternionic polynomials. We deduce from the theorem a quaternionic Bernstein's inequality and give a formulation of this last result…

This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…

We prove an improved form of an expectation of Polya and discuss several related questions

We prove new theorems which are higher-dimensional generalizations of the classical theorems of Siegel on integral points on affine curves and of Picard on holomorphic maps from $\mathbb{C}$ to affine curves. These include results on…

This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…

In this paper we give a generalization of a result of Wei.

In this note we give a detailed proof of a theorem of Aubin.

We prove a generalisation of Fernique's theorem which applies to a class of (measurable) functionals on abstract Wiener spaces by using the isoperimetric inequality. Our motivation comes from rough path theory where one deals with iterated…

A special theorem related to the Fagnano's problem is proved and an example of the theorem is shown in a golden rectangle.