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Motivated by a partition inequality of Bessenrodt and Ono, we obtain analogous inequalities for $k$-colored partition functions $p_{-k}(n)$ for all $k\geq2$. This enables us to extend the $k$-colored partition function multiplicatively to a…
We establish a new decoupling inequality for curves in the spirit of [B-D1], [B-D2] which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method as developed further in [H]. In particular, this…
On a convex bounded open set, we prove that Poincar\'e-Sobolev constants for functions vanishing at the boundary can be bounded from below in terms of the norm of the distance function in a suitable Lebesgue space. This generalizes a result…
The aim of this paper is to introduce and to investigate the basic properties of $q$-convex, $q$-affine and $q$-concave sequences and to establish their surprising connection to Chebyshev polynomials of the first and of the second kind. One…
In this article we improve a lower bound for $\sum_{j=1}^k\beta_j$ (a Berezin-Li-Yau type inequality) in [E. M. Harrell II and S. Yildirim Yolcu, Eigenvalue inequalities for Klein-Gordon Operators, J. Funct. Analysis, 256(12) (2009)…
We review some recent results concerning lower eigenvalues estimates for the Dirac operator [6, 7]. We show that Friedrich's inequality can be improved via certain well-chosen symmetric tensors and provide an application to Sasakian spin…
In this paper we are focusing on functional inequalities on compact simple edge spaces. More precisely we address the question whether the classical functional inequalities (Sobolev, Poincar\'e) hold in this setting, and as a by-product of…
We investigate a type of Hermite orthogonal polynomials on $r$ lines in the plane which have a common point at the origin and endpoints at the $r$ roots of unity and we show that their related Hermite functions are eigenfunctions of a…
We study positive solutions of the superlinear Lane-Emden inequality \(-\Delta u\ge \sigma u^q\), \(q>1\), on infinite locally finite weighted graphs and connected domains of such graphs. We first prove that solvability is equivalent to the…
In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert,…
Notions and results from quantum harmonic analysis, such as the convolution between functions and operators or between two operators, is identified as the appropriate setting for Berezin quantization and Berezin-Lieb inequalities. Based on…
Geometric function theory increasingly draws on $q$-calculus to model discrete and quantum-inspired phenomena. Motivated by this, the present paper introduces new subclasses of analytic functions: the class $\mathcal{S}^{*}_{\xi_q}$ of…
This paper establishes comprehensive stability results for quasi-variational inequalities (QVIs) under monotone perturbations of the governing operator. We prove strong convergence of both minimal and maximal solutions when sequences of…
Asymptotic expansions are derived for Gegenbauer (ultraspherical) polynomials for large order $n$ that are uniformly valid for unbounded complex values of the argument $z$, including the real interval $0 \leq z \leq 1$ in which the zeros in…
We prove that for any convex polytope $\Omega \subset \mathbb{R}^d$ which is centrally symmetric and whose faces of all dimensions are also centrally symmetric, there exists a Riesz basis of exponential functions in the space $L^2(\Omega)$.…
One may define a trilinear convolution form on the sphere involving two functions on the sphere and a monotonic function on the interval $[-1,1]$. A symmetrization inequality of Baernstein and Taylor states that this form is maximized when…
We study generalized solutions of an evolutionary equation related to a densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and find…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
Uniform bounds are developed for derivatives of solutions of the $2$-dimensional constant negative curvature equation and the Weil-Petersson metric for the Teichm\"{u}ller and moduli spaces. The dependence of the bounds on the geometry of…
We present a unified, SI-consistent framework to constrain minimal SME coefficients $a_\mu$ and $b_\mu$ using magnetically confined two-dimensional electron systems under a uniform magnetic field. Working in the nonrelativistic…