Sever Silvestru Dragomir
A counterpart of the famous Bessel's inequality for orthornormal families in real or complex inner product spaces is given. Applications for some Gruss type inequalities are also provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
A new counterpart of Bessel's inequality for orthornormal families in real or complex inner product spaces is obtained. Applications for some Gruss type results are also provided.
Some new counterparts of Bessel's inequality for orthornormal families in real or complex inner product spaces are pointed out. Applications for some Gruss type inequalities are also empahsized.
The main aim of this monograph is to survey some recent results obtained by the author related to reverses of the Schwarz, triangle and Bessel inequalities. Some Gruss' type inequalities for orthonormal families of vectors in real or complex inner product spaces are presented as well. Generalizations of the Boas-Bellman, Bombieri, Selberg, Heilbronn and Pecaric inequalities for finite sequences of vectors that are not necessarily orthogonal are also provided. Two extensions of the celebrated Ostrowski's inequalities for sequences or real numbers and the generalization of Wagner's inequality in…
Some companions of Gruss inequality in inner product spaces and applications for integrals are given.
In this paper, we obtained some new Ostrowski-Gruss type inequalities contains twice differentiable functions.
Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces that improve some earlier results are pointed out. They are applied to obtain new Gruss type inequalities in inner product spaces. Some natural applications for integral inequalities are also pointed out.
We study functional inequality of the form $$|T(f,h)-T(f,g)T(g,h)| \leq F(f,g)F(g,h) -F(f,h)$$ where $T$ is a complex-valued functional and $F$ is a real-valued map. Motivation for our studies comes from some generalizations of Grüss inequality.
New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in an earlier paper. Further, they are employed to establish new Gruss type inequalities. Finally, some natural integral inequalities are stated as well.
On some Analytic Inequalities for Gauss Hypergeometric Functions via Gruss Discrete Inequality
本文利用Grüss离散不等式研究一类高斯超几何函数的近似，为伽马和贝塔函数的扩展提供了新的解析不等式。
In this paper, using a fractional integral as proposed by Katugampola we establish a generalization of integral inequalities of Gruss-type. We prove two theorems associated with these inequalities and then immediately we enunciate and prove others inequalities associated with these fractional operator.
We prove a more general version of the Gruss inequality by using the recent theory of combined dynamic derivatives on time scales and the more general notions of diamond-alpha derivative and integral. For the particular case when alpha = 1, one gets a delta-integral Gruss inequality on time scales; for alpha = 0 a nabla-integral Gruss inequality. If we further restrict ourselves by fixing the time scale to the real (or integer) numbers, then the standard continuous (discrete) inequalities are obtained.
The classical form of Grüss' inequality, first published by G. Grüss in 1935, gives an estimate of the difference between the integral of the product and the product of the integrals of two functions. In the subsequent years, many variants of this inequality appeared in the literature. The aim of this paper is to introduce a different approach, presenting a new Chebyshev-Grüss-type inequality and applying it to different well-known linear, not necessarily positive, operators. Some conjectures are presented as well. We also compare the new inequalities with some older results. This new approach…
The classical form of Grüss' inequality was first published by G. Grüss in 1935 and gives an estimate of the difference between the integral of the product and the product of the integrals of two functions. After that many variants of this inequality appeared in the literature. The aim of this paper is to consider some Chebyshev-Grüss-type inequalities and apply them to Bernstein-Euler-Jacobi (BEJ) operators of first and second kind. First and second moments of the operators are used to explain the situation.
Assuming a unitarily invariant norm $|||\cdot|||$ is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms $|||\cdot|||$ on matrix algebras $\mathcal{M}_n$ for all finite values of $n$ via $|||A|||=|||A\oplus 0|||$. We show that if $\mathscr{A}$ is a $C^*$-algebra of finite dimension $k$ and $Φ: \mathscr{A} \to \mathcal{M}_n$ is a unital completely positive map, then \begin{equation*} |||Φ(AB)-Φ(A)Φ(B)||| \leq \frac{1}{4} |||I_{n}|||\,|||I_{kn}||| d_A d_B \end{equation*} for any $A,B \in \mathscr{A}$, where $d_X$ d…
Gruss Type Discrete Inequalities in Inner Product Spaces, Revisited
本文重新探讨内积空间中的 Gruss 型离散不等式，得到尖锐结果并应用于凸函数的 Jensen 不等式。
For a probability measure $μ$ and for square integrable fields $(\mathscr{A}_t)$ and $(\mathscr{B}_t)$ ($t\inΩ$) of commuting normal operators we prove Landau type inequality \llu\int_Ω\mathscr{A}_tX\mathscr{B}_tdμ(t)- \int_Ω\mathscr{A}_t\,dμ(t)X \int_Ω\mathscr{B}_t\,dμ(t) \rru \le \llu \sqrt{\,\int_Ω|\mathscr{A}_t|^2\dt-|\int_Ω\mathscr{A}_t\dt|^2}X \sqrt{\,\int_Ω|\mathscr{B}_t|^2 \dt-|\int_Ω\mathscr{B}_t\dt|^2} \rru for all $X\in\mathcalb{B}(\mathcal{H})$ and for all unitarily invariant norms $\lluo\cdot\rruo$. For Schatten $p$-norms similar inequalities are given for arbitrary double square …
In this work, a generalization of Chebyshev functional is presented. New inequalities of Gruss type via Pompeiu's mean value theorem are established. Improvements of some old inequalities are proved. A generalization of pre-Gruss inequality is elaborated. Some remarks to further generalization of Chebyshev functional are presented. As applications, bounds for the reverse of CBS inequality are deduced. Hardy type inequalities on bounded real interval [a,b] under some other circumstances are introduced. Other related ramified inequalities for differentiable functions are also given.
Trace inequality with Bessel convolution
本文研究了带Bessel卷积的迹不等式，通过Bessel核定义的位势给出了其Kerman-Sawyer型刻画，并以此导出了Schrödinger-Bessel算子最小特征值的估计。
The aim of this paper is to establish Turán -type inequality for the Hahn-Exton $q$-Bessel functions. The result is obtained by the use of limit transition.
On a measure-theoretic reading of $β$-Grüss-type inequalities
该研究从初等测度论解读β - 格鲁斯型不等式，将正β - 积分视为特定测度积分并归一化，利用概率空间标准事实得出相关不等式，确定了构成此类不等式族的测度论机制。
New results related to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
New results related to the Boas-Bellman generalisation of Bessel's inequality in inner product spaces are given.
We define and examine nonlinear potential by Bessel convolution with Bessel kernel. We investigate removable sets with respect to Laplace-Bessel inequality. By studying the maximal and fractional maximal measure, a Wolff type inequality is proved. Finally the relation of B-$p$ capacity and B-Lipschitz mapping, and the B-$p$ capacity and weighted Hausdorff measure and the B-$p$ capacity of Cantor sets are examined.
In the paper, the authors verify the complete monotonicity of the difference $e^{1/t}-ψ'(t)$ on $(0,\infty)$, compute the completely monotonic degree and establish integral representations of the remainder of the Laurent series expansion of $e^{1/z}$, and derive an inequality which gives a lower bound for the first order modified Bessel function of the first kind.
In this paper, an analogous of Heisenberg inequality is established for Laguerre-Bessel transform. Also, a local uncertainty principle for this transform is investigate
An order-interpolation inequality for Bessel functions
证明贝塞尔函数平方和的一个不等式，作为阶的内插，并应用于自由薛定谔方程光滑估计最优常数的维数比较。
Companion results to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
Our aim is to extend some trigonometric inequalities to Bessel functions. Moreover, we extend the hyperbolic analogue of these trigonometric inequalities. As an application of these results we present a generalization of Cusa-type inequality to modified Bessel function. Our main motivation to write this paper is a recent publication of Chen and Sándor, which we wish to complement.
We unify the three distinct inequality sequences (Abramowitz ans Stegun (1972) [1,9.5.2]) of positive real zeros of Bessel functions into a single one.
We establish good numerical estimates for a certain class of integrals involving sixfold products of Bessel functions. We use relatively elementary methods. The estimates will be used in the study of a sharp Fourier restriction inequality on the circle.
In this work we prove analogues of Bessel inequality and Riesz-Fisher theorem in Hilbert spaces with respect to sequences. We apply our generalized Bessel inequality to the Hilbert spaces associated with the Normal, Beta, Gamma and certain discrete probability distributions to show how to generate certain type of inequalities for special functions systematically.
Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double inequality, involving the modified Bessel function of the first kind, for a generalized hypergeometric function. We also present some open problems that arise from this research.
In this paper our aim is to show some new inequalities of Redheffer type for Bessel and modified Bessel functions of the first kind. The key tools in our proofs are some classical results on the monotonicity of quotients of differentiable functions as well as on the monotonicity of quotients of two power series. We use also some known results on the quotients of Bessel and modified Bessel functions of the first kind, and by using the monotonicity of the Dirichlet eta function we prove a sharp inequality for the tangent function. At the end of the paper a conjecture is stated, which may be of i…
In this paper first we survey the Turán type inequalities and related problems for the Bessel functions of the first kind. Then we extend the known higher order Turán type inequalities for Bessel functions of the first kind to real parameters and we deduce new closed integral representation formulae for the second kind Neumann type series of Bessel functions of the first kind occurring in the study of Turán determinants of Bessel functions of the first kind. At the end of the paper we prove a Turán type inequality for the Bessel functions of the second kind.
In this note our aim is to present some monotonicity properties of the product of modified Bessel functions of first and second kind. Certain bounds for the product of modified Bessel functions of first and second kind are also obtained. These bounds improve and extend known bounds for the product of modified Bessel functions of first and second kind of order zero. A new Turán type inequality is also given for the product of modified Bessel functions, and some open problems are stated, which may be of interest for further research.
Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided.
The purpose of this paper is to establish L^p error estimates, a Bernstein inequality, and inverse theorems for approximation by a space comprising spherical basis functions located at scattered sites on the unit n-sphere. In particular, the Bernstein inequality estimates L^p Bessel-potential Sobolev norms of functions in this space in terms of the minimal separation and the L^p norm of the function itself. An important step in its proof involves measuring the L^p stability of functions in the approximating space in terms of the l^p norm of the coefficients involved. As an application of the B…
In this paper we prove a sharp trilinear inequality which is motivated by a program to obtain the sharp form of the $L^2 - L^6$ Tomas-Stein adjoint restriction inequality on the circle. Our method uses intricate estimates for integrals of sixfold products of Bessel functions developed in a companion paper. We also establish that constants are local extremizers of the Tomas-Stein adjoint restriction inequality as well as of another inequality appearing in the program.
We establish a Maz'ya type capacitary inequality which resolves a special case of a conjecture by David R. Adams. As a consequence, we obtain several equivalent norms for Choquet integrals associated to Bessel or Riesz capacities. This enables us to obtain bounds for the Hardy-Littlewood maximal function in a sublinear setting.
Sharp two-sided bounds for the product of modified Bessel functions and for its logarithmic derivative
本文为修正贝塞尔函数乘积及其对数导数之和建立了带最优常数的尖锐双侧不等式，证明基于辅助函数的二阶微分不等式与强极大值原理，并应用于乘积单调性和比值改进。
Turán type inequalities for oscillatory special functions
本文证明并推广了Baricz关于第一类贝塞尔函数的Turán型不等式猜想，通过分析归一化Turán表达式的局部最小值性质，将结果推广至一般贝塞尔函数、库仑波函数等，并给出复平面包含性质。
$A_\infty$-invariance of oscillatory norms, and Schatten characterisations of commutators
本文扩展已有交换子Schatten类刻画的抽象框架，引入$A_\infty$等价测度对放宽正则性假设，用实变调和分析方法复现并简化了Bessel-Riesz变换交换子的相关刻画结果。
Weighted norm inequalities for operators with new Muckenhoupt type weights in the Bessel setting and applications
本文在贝塞尔框架下刻画新型Muckenhoupt型权的性质，推导相关算子的加权范数不等式，补充了哈代-李特尔伍德极大算子的缺失加权界，为相关算子的加权估计提供了新结果。
On domain properties of Bessel-type operators
本文研究了在区间端点具有更一般逆平方奇异性的Bessel型算子，考虑了$L^2$空间中相关微分表达式的二次型与算子实现，并具体描述了对应极小算子的Krein-von Neumann延拓。
Schatten properties of commutators of fractional integrals on spaces of homogeneous type
研究分数积分在齐型空间上交换子的Schatten性质，通过Besov空间或分数Sobolev空间的条件确定其属于$S^p$的条件。
We show that weak solutions to the strongly-coupled system of nonlocal equations of linearized peridynamics belong to a potential space with higher integrability. Specifically, we show a function that measures local fractional derivatives of weak solutions to a linear system belongs to $L^p$ for some $p > 2$ with no additional assumption other than measurability and ellipticity of coefficients. This is a nonlocal analogue of an inequality of Meyers for weak solutions to an elliptic system of equations. We also show that functions in $L^p$ whose Marcinkiewicz-type integrals are in $L^p$ in fact…
Sharp $L^2$-stability and gradient stability hierarchies of the $L^2$-Poincaré inequalities on Euclidean balls and Gaussian Poincaré inequality
研究欧几里得球和高斯测度下尖锐 $L^2$-Poincaré 不等式的稳定性，建立尖锐 $L^2$ 与梯度稳定性估计及稳定性层级，给出最优常数与等式刻画，并揭示谱间隙结构。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。