Related papers: Simultaneous Extension of Continuous and Uniformly…

There are the longstanding differences in the continuity of continuum among mathematicians. Starting from studies on a mathematical model of contact, we construct a set that is in contact everywhere by using the original idea of Dedekind's…

In this paper, we generalize a recently obtained result by Kopaliani and Zviadadze from the one-variable case to the several-variable case. Specifically, in terms of decreasing rearrangement, we characterize those exponents $p(\cdot)$ for…

Fix integers $m\ge 2$, $n\ge 1$. We prove the existence of a bounded linear extension operator for $C^{m-1,1}(\R^n)$ with operator norm at most $\exp(\gamma D^k)$, where $D := \binom{m+n-1}{n}$ is the number of multiindices of length $n$…

The metrical theory of the product of consecutive partial quotients is associated with the uniform Diophantine approximation, specifically to the improvements to Dirichlet's theorem. Achieving some variant forms of metrical theory in…

Let $\Omega\subset\mathbb{R}^n$ be an open, connected subset of $\mathbb{R}^n$, and let $F\colon\Omega-\Omega\to\mathbb{C}$, where $\Omega-\Omega=\{x-y\colon x,y\in\Omega\}$, be a continuous positive definite function. We give necessary and…

We study monotone operators in reflexive Banach spaces that are invariant with respect to a group of suitable isometric isomorphisms and we show that they always admit a maximal extension which preserves the same invariance. A similar…

Given a densely defined skew-symmetric operators A 0 on a real or complex Hilbert space V , we parametrize all m-dissipative extensions in terms of contractions $\Phi$ : H-$\rightarrow$ H + , where Hand H + are Hilbert spaces associated…

A generalization of the regular continued fractions was given by Burger et al. in 2008 [3]. In this paper we give metric properties of this expansion. For the transformation which generates this expansion, its invariant measure and…

We continue the study of the analogue of Thurston's metric on the Teichm{\"u}ller space of Euclidean triangle which was started by Saglam and Papadopoulos in [1].By direct calculation, we give explicit expressions of the distance function…

We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…

We derive a convergent expansion of the generalized hypergeometric function ${}_{p-1}F_p$ in terms of the Bessel functions ${}_{0}F_1$ that holds uniformly with respect to the argument in any horizontal strip of the complex plane. We…

A Hausdorff measure version of W.M. Schmidt's inhomogeneous, linear forms theorem in metric number theory is established. The key ingredient is a `slicing' technique motivated by a standard result in geometric measure theory. In short,…

In this paper, we aim to present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella hypergeometric functions, by using the extended Bessel function due to Boudjelkha [4].…

In this paper we establish concavity properties of two extensions of the classical notion of the outer parallel volume. On the one hand, we replace the Lebesgue measure by more general measures. On the other hand, we consider a functional…

The Lipschitz extension modulus $e(M)$ of a metric space $M$ is the infimum over $L\ge 1$ such that for any Banach space $Z$ and any $C\subset M$, any 1-Lipschitz function $f:C\to Z$ can be extended to an $L$-Lipschitz function $F:M\to Z$.…

We prove that self-similar measures on the real line are absolutely continuous for almost all parameters in the super-critical region, in particular confirming a conjecture of S-M. Ngai and Y. Wang. While recently there has been much…

In this paper we define a new type of continued fraction expansion for a real number $x \in I_m:=[0,m-1], m\in N_+, m\geq 2$: \[x = \frac{m^{-b_1(x)}}{\displaystyle 1+\frac{m^{-b_2(x)}}{1+\ddots}}:=[b_1(x), b_2(x), ...]_m. \] Then, we…

There is constructed and considered the extension of classical Diriclet operator corresponding to uniformly log-concave measure in the space of symmetric differential forms. Sufficient conditions for its essential self-adjointness in…

We consider a unique continuation problem where the Dirichlet trace of the solution is known to have finite dimension. We prove Lipschitz stability of the unique continuation problem and design a finite element method that exploits the…

We prove a generalization of van der Corput's difference theorem for sequences of vectors in a Hilbert space. This generalization is obtained by establishing a connection between sequences of vectors in the first Hilbert space with a vector…