Archiv der Mathematik最新文献

Let G be a graph, and let (lambda (G)) denote the smallest eigenvalue of G. First, we provide an upper bound for (lambda (G)) based on induced bipartite subgraphs of G. Consequently, we extract two other upper bounds, one relying on the average degrees of induced bipartite subgraphs and a more explicit one in terms of the chromatic number and the independence number of G. In particular, motivated by our bounds, we introduce two graph invariants that are of interest on their own. Finally, special attention goes to the investigation of the sharpness of our bounds in various classes of graphs as well as the comparison with an existing well-known upper bound.

In the present paper, using the theory of boundary values of analytic semigroups, we find necessary and sufficient conditions to guarantee that the operator (i(-Delta )^{{alpha }/{2}}) generates a strongly continuous semigroup in (L^p(mathbb {R}^n)).

Based on the main result presented in Bifulco and Kerner (Proc Am Math Soc 152:295–306, 2024), we derive Ambarzumian–type theorems for Schrödinger operators defined on quantum graphs.

Strong external difference families (SEDFs) are much-studied combinatorial objects motivated by an information security application. A well-known conjecture states that only one abelian SEDF with more than 2 sets exists. We show that if the disjointness condition is replaced by non-disjointness, then abelian SEDFs can be constructed with more than 2 sets (indeed any number of sets). We demonstrate that the non-disjoint analogue has striking differences to, and connections with, the classical SEDF and arises naturally via another coding application.

For an integer (dge 2), (tin mathbb {R}), and a 0-homogeneous function (Phi in C^{infty }(mathbb {R}^{d}{setminus }{0},mathbb {R})), we consider the family of Fourier multiplier operators (T_{Phi }^t) associated with symbols (xi mapsto exp (itPhi (xi ))) and prove that for a generic phase function (Phi ), one has the estimate (Vert T_{Phi }^tVert _{L^prightarrow L^p} gtrsim _{d,p, Phi }langle trangle ^{d|frac{1}{p}-frac{1}{2}|}). That is the maximal possible order of growth in (trightarrow pm infty ), according to the previous work by V. Kovač and the author and the result shows that the two special examples of functions (Phi ) that induce the maximal growth, given by V. Kovač and the author and independently by D. Stolyarov, to disprove a conjecture of Maz’ya actually exhibit the same general phenomenon.

We use bounds on bilinear forms with Kloosterman fractions and improve the error term in the asymptotic formula of Balazard and Martin (Bull Sci Math 187:Art. 103305, 2023) on the average value of the smallest denominators of rational numbers in short intervals.

Assuming that the solution is bounded from one-side, by Bernstein-type arguments, on ((M^{2},g),) we prove the local gradient estimates for a type of fully nonlinear equation from conformal geometry.

Recently, Kimura, Otake, and Takahashi proved a theorem about the vanishing of Ext of finitely generated modules over Cohen–Macaulay rings. The aim of this paper is to obtain extensions of their result over algebras.

In this paper, we study operator mean inequalities for the weighted arithmetic, geometric, and harmonic means. We give a slight modification of Audenaert’s result to show the relation between Kwong functions and operator monotone functions. Operator mean inequalities provide some analogs of the geometric concavity property for Kwong functions, operator convex, and operator monotone functions. Moreover, we give our points across by way of some examples which show the usage of our main results.