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HYBRID SUP-NORM BOUNDS FOR HECKE-MAASS CUSP FORMS
Cutting-edge characteristic value hyperbolic measure
2015/8/25
Let f be a Hecke–Maass cusp form of eigenvalue λ and square-free level N. Normalize the hyperbolic measure such that vol(Y0(N)) = 1 and the form f such that kfk2 = 1. It is shown that kfk1 ≪1...
Subharmonic functions and performance bounds on linear time-invariant feedback systems
Harmonic function linear the performance of the single output system a linear control system the harmonic function
2015/8/13
In this paper we study multi-input multi-output (MIMO) linear time-invariant (LTI) control systems. We show that some well known constraints on the performance of single-input single-output (SISO) lin...
Upper bounds on algebraic connectivity via convex optimization
Laplace operator matrix algebra connection Laplacian invariant subset matrix convex function
2015/8/10
The second smallest eigenvalue of the Laplacian matrix L of a graph is called its algebraic connectivity. We describe a method for obtaining an upper bound on the algebraic connectivity of a family of...
Performance bounds and suboptimal policies for linear stochastic control via LMIs
dynamic programming stochastic control convex optimization
2015/8/7
In a recent paper, the authors showed how to compute performance bounds for infinite horizon stochastic control problems with linear system dynamics and arbitrary constraints, objective, and noise dis...
A frequency function and singular set bounds for branched minimal immersions
frequency function singular branched minimal immersions
2011/2/25
In [Wic08], the second author established a local C1,α partial regularity theory for stable
branched minimal hypersurfaces of multiplicity < 3. The main regularity theorem of [Wic08] in particular im...
Improved bounds for Stein's square functions
Square functions Bochner–Riesz means Wave and Schr¨odinger semigroup
2011/1/20
We prove a weighted norm inequality for the maximal Bochner–Riesz operator and the associated square-function. This yields new Lp(Rd) bounds on classes of radial Fourier multipliers for p 2 + 4/d wi...
Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function
suprema of Gaussian processes omega results random multiplicative function
2011/1/17
We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. Unlike many existing bounds, our results are not asymptotic,but supply strong information when one is only ...
Improved Lower Bounds for Ginzburg-Landau Energies via Mass Displacement
Ginzburg-Landau Energies Mass Displacement
2010/11/24
We prove some improved estimates for the Ginzburg-Landau energy (with or without magnetic field) in two dimensions, relating the asymptotic energy of an arbitrary configuration to its vortices and th...
Asymptotic Approximationof Jacobi Functions and Their Zeros with Error Bounds
Asymptotic approximation Jacobi function Zero Error bounds
2007/12/12
The study of zeros of orthogonal functions is an important topic. In this paper, by improving the middle variable $x(t)$, we've got a new form of asymptotic approximation, completed with error bounds,...
ERROR BOUNDS FOR GLIMM DIFFERENCE APPROXIMATIONS FOR SCALAR CONSERVATION LAWS WITHOUT CONVEXITY
error bounds Glimm's scheme non-convexity
2007/12/12
In last century, D. Hoff and J. Smoller derived the error bounds for the Glimm difference approximations of the solutions to scalar conservation laws with convexity. Our work is to extend the correspo...