We show that for a given holomorphic noncharacteristic surface S ∈ C, and a given holomorphic function on S, there exists a unique meromorphic solution of Burgers’ equation which blows up on S. This proves the convergence of the formal Laurent series expansion found by the Painlevé test. The method used is an adaptation of Nirenberg’s iterative proof of the abstract Cauchy-Kowalevski theorem. A...

1. Calculus on spheres 2. Spherical Laplacian from Euclidean 3. Eigenvectors for the spherical Laplacian 4. Invariant integrals on spheres 5. L spectral decompositions on spheres 6. Sup-norms of spherical harmonics on Sn−1 7. Pointwise convergence of Fourier-Laplace series 8. Irreducibility of representation spaces for O(n) 9. Hecke’s identity • Appendix: Bernstein’s proof of Weierstraß approxi...

Abstruct-The finite sample performance of a nearest neighbor classifier is analyzed for a two-class pattern recognition problem. An exact integral expression is derived for the m-sample risk R, given that a reference m-sample of labeled points is available to the classifier. The statistical setup assumes that the pattern classes arise in nature with fixed a priori probabilities and that points ...

We develop two new multivariate statistical dependence measures. The first, based on the Kullback-Leibler distance, results in a single value that indicates the general level of dependence among the random variables. The second, based on an orthonormal series expansion of joint probability density functions, provides more detail about the nature of the dependence. We apply these dependence meas...

The present work is a sequel to the papers [3] and [4], and it aims at introducing and investigating a new generalized double zeta function involving the Riemann, Hurwitz, Hurwitz-Lerch and Barnes double zeta functions as particular cases. We study its properties, integral representations, differential relations, series expansion and discuss the link with known results.

This paper presents a series expansion for the evolution of nonlinear systems which are analytic in the state and linear in the controls. An explicit recursive expression is obtained assuming that the input vector fields are constant. Additional simplifications take place in the analysis of systems described by second order polynomial vector fields. Sufficient conditions are derived to guarante...

This paper presents a series expansion for the evolution of a class of nonlinear systems characterized by constant input vector fields. We present a series expansion that can be computed via explicit recursive expressions, and we derive sufficient conditions for uniform convergence over the finite and infinite time horizon. Furthermore, we present a simplified series and convergence analysis fo...

The paper is devoted to study the H-function defined by the Mellin-Barnes integral H p,q (z) = 1 2πi ∫ L H m,n p,q (s)z ds, where the function H p,q (s) is a certain ratio of products of Gamma functions with the argument s and the contour L is specially chosen. The conditions for the existence of Hm,n p,q (z) are discussed and explicit power and power-logarithmic series expansions of Hm,n p,q (...

In this article we propose a new and so-called holomorphic deformation scheme for locally convex algebras and Hopf algebras. Essentially we regard converging power series expansion of a deformed product on a locally convex algebra, thus giving the means to actually insert complex values for the deformation parameter. Moreover we establish a topological duality theory for locally convex Hopf alg...

The cubic Hénon-Heiles system contains parameters, for most values of which, the system is not integrable. In such parameter regimes, the general solution is expressible in formal expansions about arbitrary movable branch points, the so-called psi-series expansions. In this paper, the convergence of known, as well as new, psi-series solutions on real time intervals is proved, thereby establishi...