共查询到20条相似文献,搜索用时 31 毫秒
1.
We give some characterization theorems for the D w -Laguerre-Hahn linear functionals and we extend the concept of the class of the usual Laguerre-Hahn functionals to the D w -Laguerre-Hahn functionals, recovering the classic results when w tends to zero. Moreover, we show that some transformations carried out on the D w -Laguerre-Hahn linear functionals lead to new D w -Laguerre-Hahn linear functionals. Finally, we analyze the class of the resulting functionals and we give some applications relative to the first associated Charlier, Meixner, Krawtchouk and Hahn orthogonal polynomials. 相似文献
2.
Erwin Lutwak Deane Yang Gaoyong Zhang 《Transactions of the American Mathematical Society》2001,353(5):1767-1779
New affine invariant functionals for convex polytopes are introduced. Some sharp affine isoperimetric inequalities are established for the new functionals. These new inequalities lead to fairly strong volume estimates for projection bodies. Two of the new affine isoperimetric inequalities are extensions of Ball's reverse isoperimetric inequalities.
3.
Fanwei Meng Angelo B. Mingarelli 《Proceedings of the American Mathematical Society》2003,131(3):897-904
We establish new oscillation criteria for linear Hamiltonian systems using monotone functionals on a suitable matrix space. In doing so we develop new criteria for oscillation involving general monotone functionals instead of the usual largest eigenvalue. Our results are new even in the particular case of self-adjoint second order differential systems.
4.
F. Marcellán M. Sghaier M. Zaatra 《Journal of Difference Equations and Applications》2013,19(1):162-178
In this paper, we obtain all the symmetric semi-classical linear functionals of class three taking into account the irreducible expression of the corresponding Pearson equation. We focus our attention on their integral representations. Thus, some linear functionals very well known in the literature, associated with perturbations of semi-classical linear functionals of class one at most, appear as well as new linear functionals which have not been studied. 相似文献
5.
This paper extends the Riemannian convexity concept to action functionals defined by multiple integrals associated to Lagrangian
differential forms on first order jet bundles. The main results of this paper are based on the geodesic deformations theory
and their impact on functionals in Riemannian setting. They include the basic properties of Riemannian convex functionals,
the Riemannian convexity of functionals associated to differential m-forms or to Lagrangians of class C
1 respectively C
2, the generalization to invexity and geometric meaningful convex functionals. Riemannian convexity of functionals is the central
ingredient for global optimization. We illustrate the novel features of this theory, as well as its versatility, by introducing
new definitions, theorems and algorithms that bear upon the currently active subject of functionals in variational calculus
and optimal control. In fact so deep rooted is the convexity notion that nonconvex problems are tackled by devising appropriate
convex approximations. 相似文献
6.
《Nonlinear Analysis: Theory, Methods & Applications》2004,57(4):485-504
In this paper, a new Morse index theory for strongly indefinite functionals was developed via Gălerkin approximation. In particular, the abstract theory is valid for those kinds of strongly indefinite functionals corresponding to wave equation and beam equation. 相似文献
7.
E. A. Dorofeev 《Journal of Mathematical Sciences》1999,93(3):321-335
One of the most rapidly growing fields in the theory of random processes is asymptotics of multidimensional Wiener functionals,
including such functionals as winding angles or radius-vectors of planar processes. We present a new method yielding a large
number of results on upper and lower functions for such functionals. Bibliography: 23 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 228, 1996, pp. 111–134. 相似文献
8.
By use of monotone functionals and positive linear functionals, a generalized Riccati transformation and the general means technique, some new oscillation criteria for the following self-adjoint Hamiltonian matrix system
(E) 相似文献
9.
Frank H Clarke 《Advances in Mathematics》1981,40(1):52-67
The purpose of this article is threefold: (i) to present in a unified fashion the theory of generalized gradients, whose elements are at present scattered in various sources; (ii) to give an account of the ways in which the theory has been applied; (iii) to prove new results concerning generalized gradients of summation functionals, pointwise maxima, and integral functionals on subspaces of L∞. These last-mentioned formulas are obtained with an eye to future applications in the calculus of variations and optimal control. Their proofs can be regarded as applications of the existing theory of subgradients of convex functionals as developed by Rockafellar, Ioffe and Levin, Valadier, and others. 相似文献
10.
T. Hida 《Applied Mathematics and Optimization》1984,12(1):115-123
The purpose of this paper is two-fold; i) a new class of generalized Brownian functionals, in fact generalized linear functionals, is introduced and ii) generalized stochastic integrals based on creation operators are discussed. These topics are in line with the causal calculus of Brownian functionals.Communicated by H. H. Kuo 相似文献
11.
We prove a new class of inequalities, yielding bounds for the normal approximation in the Wasserstein and the Kolmogorov distance of functionals of a general Poisson process (Poisson random measure). Our approach is based on an iteration of the classical Poincaré inequality, as well as on the use of Malliavin operators, of Stein’s method, and of an (integrated) Mehler’s formula, providing a representation of the Ornstein-Uhlenbeck semigroup in terms of thinned Poisson processes. Our estimates only involve first and second order difference operators, and have consequently a clear geometric interpretation. In particular we will show that our results are perfectly tailored to deal with the normal approximation of geometric functionals displaying a weak form of stabilization, and with non-linear functionals of Poisson shot-noise processes. We discuss two examples of stabilizing functionals in great detail: (i) the edge length of the k-nearest neighbour graph, (ii) intrinsic volumes of k-faces of Voronoi tessellations. In all these examples we obtain rates of convergence (in the Kolmogorov and the Wasserstein distance) that one can reasonably conjecture to be optimal, thus significantly improving previous findings in the literature. As a necessary step in our analysis, we also derive new lower bounds for variances of Poisson functionals. 相似文献
12.
We prove infinite-dimensional second order Poincaré inequalities on Wiener space, thus closing a circle of ideas linking limit theorems for functionals of Gaussian fields, Stein's method and Malliavin calculus. We provide two applications: (i) to a new “second order” characterization of CLTs on a fixed Wiener chaos, and (ii) to linear functionals of Gaussian-subordinated fields. 相似文献
13.
Long-range dependent random fields with spectral densities, which are unbounded at some frequencies, are investigated. We demonstrate new examples of covariance functions, which do not exhibit a regular varying asymptotic behavior at infinity. However, the variances of averaged functionals of these fields are regularly varying. The limit theorems for weighted functionals of cyclic long-range dependent fields are obtained. The order of normalizing constants and relations between the weight functions and singularities in non-degenerative asymptotics are discussed. 相似文献
14.
Volker Krätschmer 《Journal of multivariate analysis》2012,103(1):35-47
The main goal of this article is to introduce a new notion of qualitative robustness that applies also to tail-dependent statistical functionals and that allows us to compare statistical functionals in regards to their degree of robustness. By means of new versions of the celebrated Hampel theorem, we show that this degree of robustness can be characterized in terms of certain continuity properties of the statistical functional. The proofs of these results rely on strong uniform Glivenko-Cantelli theorems in fine topologies, which are of independent interest. We also investigate the sensitivity of tail-dependent statistical functionals w.r.t. infinitesimal contaminations, and we introduce a new notion of infinitesimal robustness. The theoretical results are illustrated by means of several examples including general L- and V-functionals. 相似文献
15.
This paper is devoted to the study of direct and inverse (Laurent) polynomial modifications of moment functionals on the unit circle, i.e., associated with hermitian Toeplitz matrices. We present a new approach which allows us to study polynomial modifications of arbitrary degree.The main objective is the characterization of the quasi-definiteness of the functionals involved in the problem in terms of a difference equation relating the corresponding Schur parameters. The results are presented in the general framework of (non-necessarily quasi-definite) hermitian functionals, so that the maximum number of orthogonal polynomials is characterized by the number of consistent steps of an algorithm based on the referred recurrence for the Schur parameters.The non-uniqueness of the inverse problem makes it more interesting than the direct one. Due to this reason, special attention is paid to the inverse modification, showing that different approaches are possible depending on the data about the polynomial modification at hand. These different approaches are translated as different kinds of initial conditions for the related inverse algorithm.Some concrete applications to the study of orthogonal polynomials on the unit circle show the effectiveness of this new approach: an exhaustive and instructive analysis of the functionals coming from a general inverse polynomial perturbation of degree one for the Lebesgue measure; the classification of those pairs of orthogonal polynomials connected by a certain type of linear relation with constant polynomial coefficients; and the determination of those orthogonal polynomials whose associated ones are related to a degree one polynomial modification of the original orthogonality functional. 相似文献
16.
Permanents of matrices with random elements are studied. For random permanents of finitedimensional projection matrices, new limiting results are obtained in different asymptotic schemes. The principal statistical functionals such asU-statistics, symmetric statistics, and others, are represented as functionals of permanent measures.Part of this research was supported by the Fund for Fundamental Researches of Ukrainian State Committee of Science and Technology. 相似文献
17.
A new approach to the optimal control of diffusion processes based on Lagrange functionals is presented. The method is conceptually and technically simpler than existing ones. A first class of functionals allows to obtain optimality conditions without any resort to stochastic calculus and functional analysis. A second class, which requires Ito's rule, allows to establish optimality in a larger class of problems. Calculations in these two methods are sometimes akin to those in minimum principles and in dynamic programming, but the thinking behind them is new. A few examples are worked out to illustrate the power and simplicity of this approach.Research performed at the Mathematisches Seminar der Universität Kiel with support provided by an Alexander von Humboldt Foundation fellowship. 相似文献
18.
Emmanuel Giner 《Journal of Mathematical Analysis and Applications》2012,394(1):13-29
In this work, with the introduction in the -finite case of a modulus of equi-integrability, we prove some new extensions of Fatou’s lemma and some of its consequences in the convergence theory of integral functionals. We present the case of a sequence of integral functionals using an analog of Ioffe’s criterion for a sequence of integrands. 相似文献
19.
Yu. A. Davydov 《Journal of Mathematical Sciences》1987,36(4):468-473
One presents a new method for isolating conditions for the absolute continuity of distributions of functionals of random processes. The obtained general result is applied to the investigation of integral functionals of stationary processes, to the supremum of semistable processes, and to the norm of stable Banach-valued vectors.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 142, pp. 48–54, 1985. 相似文献
20.
L. B. Knyazhishche 《Differential Equations》2012,48(10):1354-1363
We present new tests for the stability and asymptotic stability of trivial solutions of equations with deviating argument of the neutral type. Unlike well-known results, here we use nonmonotone indefinite Lyapunov functionals. Our class of functionals contains both Lyapunov-Krasovskii functionals and Lyapunov-Razumikhin functions as natural special cases. This class of functionals is broad enough that, in a number of stability tests, we have been able to omit the a priori requirement of stability of the corresponding difference operator. In addition, we present tests for the asymptotic stability of solutions of equations of the neutral type with unbounded right-hand side and new estimates for the magnitude of perturbations that do not violate the asymptotic stability if it holds for the unperturbed equation. The obtained estimates single out domains of the phase space in which perturbations should be small and domains in which essentially no constraints are imposed on the perturbation magnitude. 相似文献