Mediterranean Journal of Mathematics最新文献

Based on a generalization of the Krasnoselskii’s fixed point theorem and Avery–Peterson fixed point theorem, the object of this paper is to investigate the existence of positive solutions to a second-order Sturm–Liouville problem with derivative term and nonlocal boundary conditions. Also, some examples are given to illustrate our main results.

In this paper, we completely characterize (L^{p,q})-boundedness of (maximal) Fock projections on (mathbb {C}) for (1le p,qle infty ). As applications, we identify the dual space of mixed norm space (F_alpha ^{p,q}) of entire functions and present an alternative proof of the Littlewood–Paley formula for (F_alpha ^{p,q}).

In this paper, we study the (ell ^p)-maximal regularity for the fractional difference equation with finite delay:

where A and B are bounded linear operators defined on a Banach space X, (f:{mathbb {N}}_0rightarrow X) is an X-valued sequence and (2<alpha <3). We introduce an operator theoretical method based on the notion of (alpha )-resolvent sequence of bounded linear operators, which gives an explicit representation of solution. Further, using Blunck’s operator-valued Fourier multipliers theorems on (ell ^p(mathbb {Z}; X)), we completely characterize the (ell ^p)-maximal regularity of solution when (1< p < infty ) and X is a UMD space.

This paper introduces a method to detect each geometrically significant loop that is a geodesic circle (an isometric embedding of (S^1)) and a bottleneck loop (meaning that each of its perturbations increases the length) in a geodesic space using persistent homology. Under fairly mild conditions, we show that such a loop either terminates a 1-dimensional homology class or gives rise to a 2-dimensional homology class in persistent homology. The main tool in this detection technique are selective Rips complexes, new custom made complexes that function as an appropriate combinatorial lens for persistent homology to detect the above mentioned loops. The main argument is based on a new concept of a local winding number, which turns out to be an invariant of certain homology classes.

The paper is concerned with a nonlocal problem for a partial Fredholm integro-differential equation (IDE) of hyperbolic type is investigated. This problem is reduced to a problem containing a family of boundary value problems for the ordinary Fredholm IDEs and some integral relationships. A novel concept of general solution to a family of the ordinary Fredholm IDEs is introduced, and its properties are discussed. A necessary and sufficient condition for the well-posedness of the nonlocal problem for the partial Fredholm integro-differential equation (IDE) of hyperbolic type is obtained, and an algorithm for finding its solution is offered.

We prove that on every compact Riemann surface M, there is a Cantor set (C subset M) such that (M{ setminus }C) admits a proper conformal constant mean curvature one ((text {CMC-1})) immersion into hyperbolic 3-space (mathbb {H}^3). Moreover, we obtain that every bordered Riemann surface admits an almost proper (text {CMC-1}) face into de Sitter 3-space (mathbb {S}_1^3), and we show that on every compact Riemann surface M, there is a Cantor set (C subset M) such that (M {setminus } C) admits an almost proper (text {CMC-1}) face into (mathbb {S}_1^3). These results follow from different uniform approximation theorems for holomorphic null curves in (mathbb {C}^2 times mathbb {C}^*) that we also establish in this paper.

Quasiordinary power series were introduced by Jung at the beginning of the 20th century, and were not paid much attention until the work of Lipman and, later on, Gao. They have been thoroughly studied since, as they form a very interesting family of singular varieties, whose properties (or at least many of them) can be encoded in a discrete set of integers, much as what happens with curves. Hironaka proposed a generalization of this concept, the so-called (nu )-quasiordinary power series, which has not been examined in the literature in such detailed way. This paper explores the behavior of these series under the resolution process in the surface case.

The GNS construction for positive invariant sesquilinear forms on quasi *-algebra ((mathfrak A,{mathfrak A}_{scriptscriptstyle 0})) is generalized to a class of positive sesquilinear maps from (mathfrak Atimes mathfrak A) into a (C^*)-algebra ({mathfrak {C}}). The result is a *-representation taking values in a space of operators acting on a certain quasi-normed ({mathfrak {C}})-module.

In this paper, we consider (mathcal {E}) the set of all infinitely differentiable functions with compact support included on the interval (I=[-1,1]). We use the distributions in (mathcal {E}), as a tool to prove the continuity of the Dunkl operator and the Dunkl translation. Some properties of the modulus of smoothness related to the Dunkl operator are verified. By means of generalized Dunkl–Lipschitz conditions on Dunkl–Sobolev spaces, a result of Younis on the torus, which is an analog of Titchmarsh’s theorem, is deduced as a special case. In addition, certain conditions and a characterization of the Dini–Lipschitz classes on I in terms of the behavior of their Fourier–Dunkl coefficients are derived.

A subgroup H of the circle group ({mathbb {T}}) is called characterized by a sequence of integers ((u_n)) if (H={xin {mathbb {T}}: lim _{nrightarrow infty } u_nx=0}). In this note, we primarily consider a non-arithmetic sequence arising out of an arithmetic sequence in line of Bíró et al. (Stud Sci Math Hung 38: 97–113, 2001) and investigate the corresponding characterized subgroup thoroughly which includes its cardinality aspects. The whole investigation reiterates that these characterized subgroups are infinitely generated unbounded torsion countable subgroups of the circle group ({mathbb {T}}). Finally, we delve into certain structure theoretic observations.