Quadratic Functionals of nth Order

Principal Quadratic Functionals and Self-Adjoint Second-Order Differential Equations.

MORE ON OSCILLATION OF nTH-ORDER EQUATIONS

In this paper we prove that a higher-order differential equation with one middle term has every bounded solution oscillatory. Moreover, the behavior of unbounded solutions is given. Two other results dealing with positive solutions are also given.

Oscillations of Nth-order Functional Differential Equations

-Some new oscillation criteria for the even order damped functional differential equation (a(t)z(n-1)(t)) ' ÷ p(t)lz(n-1)(Ol#x(n-a)(O ÷ q(t)f(xIaa(t)] . . . . . =Lq.~(t)]) = 0 are established, where ~ _> O. These criteria are an extension of some of the known results. 1. I N T R O D U C T I O N Recently, Grace and Lalli [1] discussed the oscillation of the nth-order functional differential equa...

Minimax Estimation of Quadratic Fourier Functionals

We study estimation of (semi-)inner products between two nonparametric probability distributions, given IID samples from each distribution. These products include relatively well-studied classical L and Sobolev inner products, as well as those induced by translation-invariant reproducing kernels, for which we believe our results are the first. We first propose estimators for these quantities, a...

Singular quadratic functionals of one dependent variable

Singular quadratic functionals of one dependent variable with nonseparated boundary conditions are investigated. Necessary and sufficient conditions for nonnegativity of these functionals are derived using the concept of coupled point and singularity condition. The paper also includes two comparison theorems for coupled points with respect to the various boundary conditions.