Lp - Logistic discrimination

The paper presents L_p-solution for logistic discriminant function in dichotomous as well as in the polychotomous problem.     

关于L_p球的几个新不等式和性质(英文)

本文研究了L_p球的相关问题.利用对偶混合体积、球面Radon变换和Fourier变换的方法,获得了关于L_p球的几个新不等式和性质,其中一个不等式与著名的最大切片猜想有关.     

Local Lp-saturation of positive linear convolution operators

The approximation of unbounded functions by positive linear operators under multiplier enlargement is investigated. It is shown that a very wide class of positive linear operators can be used to approximate functions with arbitrary growth on the real line. Estimates are given in terms of the usual quantities which appear in the Shisha-Mond theorem. Examples are provided.     

On the stationary Lp-approximation power to derivatives by radial basis function interpolation

In this paper, we consider approximation to derivatives of a function by using radial basis function interpolation. Most of well-known theories for this problem provide error analysis in terms of the so-called native space, say C_φ. However, if a basis function φ is smooth, the space C_φ is extremely small. Thus, the purpose of this study is to extend this result to functions in the homogenous Sobolev space.     

Lp-Approximable Sequences of Vectors and Limit Distribution of Quadratic Forms of Random Variables

The properties of L₂-approximable sequences established here form a complete toolkit for statistical results concerning weighted sums of random variables, where the weights are nonstochastic sequences approximated in some sense by square-integrable functions and the random variables are “two-wing” averages of martingale differences. The results constitute the first significant advancement in the theory of L₂-approximable sequences since 1976 when Moussatat introduced a narrower notion of L₂-generated sequences. The method relies on a study of certain linear operators in the spaces L_p and l_p. A criterion of L_p-approximability is given. The results are new even when the weight generating function is identically 1. A central limit theorem for quadratic forms of random variables illustrates the method.     

Best Lp approximate solutions of nonlinear integrodifferential equations

In this paper best L_p approximate solutions are shown to exist for a wide class of integrodifferential equations. Using approximation theory techniques, a local existence theorem for solutions is established, and the convergence of the best approximate solutions to a solution is shown.     

Degree of Lp-approximation by certain positive convolution operators

The degree of L_p-approximation for a class of positive convolution operators is investigated. Recent results of De Vore, Bojanic, and Shisha for the uniform approximation by these operators and the K-functional of Peetre are employed to obtain the degree of approximation in terms of the integral modulus of smoothness.     

On analytic and coanalytic function spaces Cp(X)

Under the assumption (V = L) we construct countable completely regular spaces X and Y such that the spaces C_p(X) and C_p(Y) of real-valued continuous functions on X and Y, equipped with the pointwise convergence topology, are analytic noncoanalytic and they are not homeomorphic. We also give analogous examples of coanalytic nonanalytic function spaces.     

On Lp-Generalization of a Theorem of Adamyan, Arov, and Kreın

The paper deals with problems relating to the theory of Hankel operators. Let G be a bounded simple connected domain with the boundary Γ consisting of a closed analytic Jordan curve. Denote by _n,p(G), 1p<∞, the class of all meromorphic functions on G that can be represented in the form h=β/α, where β belongs to the Smirnov class E_p(G), α is a polynomial degree at most n, α0. We obtain estimates of s-numbers of the Hankel operator A_f constructed from fL_p(Γ), 1p<∞, in terms of the best approximation Δ_n,p of f in the space L_p(Γ) by functions belonging to the class _n,p(G).     

Asymptotics for Lp extremal polynomials on the unit circle

Let p > 1, and dμ a positive finite Borel measure on the unit circle Γ: = {z ε C: ¦z¦ = 1}. Define the monic polynomial φ_{n, p}(z)=zⁿ+…εP_n >(the set of polynomials of degree at most n) satisfying

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. Under certain conditions on dμ, the asymptotics of φ_{n, p}(z) for z outside, on, or inside Γ are obtained (cf. Theorems 2.2 and 2.4). Zero distributions of φ_{n, p} are also discussed (cf. Theorems 3.1 and 3.2).     

Minimal Lp projections by Fourier, Taylor, and Laurent series

In appropriate function space settings, it is proved that the Fourier, Taylor, and Laurent series projections are minimal in all L_p norms (1 p ∞). This result unifies and extends known results for the Fourier, Taylor, and Laurent projections in L_∞ and for the Fourier projection in L₁. The proof is based on a generalisation of a kernel summation formula due to Berman.     

Constrained Lp-Approximation by Generalized n-Convex Functions Induced by ECT-Systems

The problem of finding a best L_p-approximation (1 ≤ p < ∞) to a function in L_p from a special subcone of generalized n-convex functions induced by an ECT-system is considered. Tchebycheff splines with a countably infinite number of knots are introduced and best approximations are characterized in terms of local best approximations by these splines. Various properties of best approximations and their uniqueness in L₁ are investigated. Some special results for generalized monotone and convex cases are obtained.     

Lp-continuous extreme selectors of multifunctions with decomposable values: Existence theorems

The existence theorems of L _p -continuous selectors that values are extreme points are proved for a class of multivalued maps. Applications to multivalued maps appearing in multivalued differential equations are presented.Supported in part by RFFI Grant 93-011-264.