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We present some upper and lower bounds for the numerical radius of a bounded linear operator defined on complex Hilbert space, which improves on the existing upper and lower bounds. We also present an upper bound for the spectral radius of…

Functional Analysis · Mathematics 2024-08-13 Pintu Bhunia , Santanu Bag , Kallol Paul

In this paper, we give a new generalization of the Bohr inequality in refined form both for bounded analytic functions, and for sense-preserving harmonic functions with analytic part being bounded.

Complex Variables · Mathematics 2021-04-15 Saminathan Ponnusamy , Ramakrishnan Vijayakumar

For $L^2$-normalized joint eigenfunctions in a quantum integrable system, [GT20] gave polynomial improvements over the standard H\"omander bounds for typical points. In this paper, we improve their result by establishing a sharp bound of…

Analysis of PDEs · Mathematics 2026-04-27 Xianchao Wu , Xiao Xiao

This paper is devoted to providing quantitative bounds on the location of eigenvalues, both discrete and embedded, of non self-adjoint Lam\'e operators of elasticity $-\Delta^\ast + V$ in terms of suitable norms of the potential $V$. In…

Spectral Theory · Mathematics 2021-01-26 Biagio Cassano , Lucrezia Cossetti , Luca Fanelli

For a Legendre-Galerkin semi-discretization of the 1-D homogeneous wave equation, the high frequency components of the numerical solution prevent us from obtaining the boundary observability (inequality), uniformly with regard to the…

Optimization and Control · Mathematics 2016-12-02 Ludovick Gagnon , José Urquiza

We give a new bound on the sum of the linear Fourier coefficients of a Boolean function in terms of its parity decision tree complexity. This result generalizes an inequality of O'Donnell and Servedio for regular decision trees. We use this…

Discrete Mathematics · Computer Science 2015-06-04 Eric Blais , Li-Yang Tan , Andrew Wan

We derive explicit expressions for the sum rules of the eigenvalues of inhomogeneous strings with arbitrary density and with different boundary conditions. We show that the sum rule of order $N$ may be obtained in terms of a diagrammatic…

Mathematical Physics · Physics 2015-06-15 Paolo Amore

Cooperative spectrum sensing based on the limiting eigenvalue ratio of the covariance matrix offers superior detection performance and overcomes the noise uncertainty problem. While an exact expression exists, it is complex and multiple…

Signal Processing · Electrical Eng. & Systems 2019-09-04 Fuhui Zhou , Norman C. Beaulieu

A key quantity that occurs in the error analysis of several numerical methods for eigenvalue problems is the distance between the eigenvalue of interest and the next nearest eigenvalue. When we are interested in the smallest or fundamental…

Numerical Analysis · Mathematics 2024-12-20 Alexander D. Gilbert , Ivan G. Graham , Robert Scheichl , Ian H. Sloan

We investigate isoperimetric upper bounds for sums of consecutive Steklov eigenvalues of planar domains. The normalization involves the perimeter and scale-invariant geometric factors which measure deviation of the domain from roundness. We…

Spectral Theory · Mathematics 2016-01-27 A. Girouard , R. S. Laugesen , B. A. Siudeja

In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the…

Probability · Mathematics 2012-02-09 Alexander Goldenshluger , Oleg Lepski

Uniform bounds are obtained using the auxiliary Monge-Amp\`ere equation method for solutions of very general classes of fully non-linear partial differential equations, assuming the existence of a ${C}$-subsolution in the sense of G.…

Analysis of PDEs · Mathematics 2024-01-23 Bin Guo , Duong H. Phong

We give some new bounds for the clique and independence numbers of a graph in terms of its eigenvalues.

Combinatorics · Mathematics 2017-01-31 Vladimir Nikiforov

In this paper we express the eigenvalues of a sort of real heptadiagonal symmetric matrices as the zeros of explicit rational functions establishing upper and lower bounds for each of them. From these prescribed eigenvalues we compute also…

Rings and Algebras · Mathematics 2019-07-17 João Lita da Silva

The primary aim of this paper is to establish bounds on the joint spectral radius for a finite set of nonnegative matrices based on their diagonal elements. The efficacy of this approach is evaluated in comparison to existing and related…

Combinatorics · Mathematics 2025-07-15 Vuong Bui

In this paper, we study the spectral problem on a compact Finsler manifold with or without boundary. More precisely, given a certain collection of sets in Sobolev space $H^{1,2}(M)$ and a dimension-like function, we can define a…

Differential Geometry · Mathematics 2019-07-02 Zhongmin Shen , Wei Zhao

As a continuation of our previous work \cite{KV2} the aim of the recent paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral synthesis in translation invariant closed linear subspaces…

Complex Variables · Mathematics 2017-04-18 Gergely Kiss , Csaba Vincze

In this work, we introduce a new difference equation which is discrete analogue of Diffusion differential equation and analyze some essential spectral properties, Diffusion difference operator is self-adjoint, eigenvalues of this problem…

Spectral Theory · Mathematics 2017-05-03 Erdal Bas , Ramazan Ozarslan

We compute the spectral statistics of the sum H of two independent complex Wishart matrices, each of which is correlated with a different covariance matrix. Random matrix theory enjoys many applications including sums and products of random…

Mathematical Physics · Physics 2016-07-05 Gernot Akemann , Tomasz Checinski , Mario Kieburg

For smooth bounded domains in $\mathbb{R}$, we prove upper and lower $L^2$ bounds on the boundary data of Neumann eigenfunctions, and prove quasi-orthogonality of this boundary data in a spectral window. The bounds are tight in the sense…

Analysis of PDEs · Mathematics 2018-11-14 Alex Barnett , Andrew Hassell , Melissa Tacy