Related papers: Some characterizations of the spherical harmonics …
Outliers contaminating data sets are a challenge to statistical estimators. Even a small fraction of outlying observations can heavily influence most classical statistical methods. In this paper we propose generalized spherical principal…
This Note presents the resolution of a differential system on the plane that translates a geometrical problem about isotropic deformations of area and length. The system stems from a probability study on deformed random fields [J.Fournier…
Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and…
The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equation relating the coefficients that dictate the frame motion.…
In the present paper we survey the most recent classification results for proper biharmonic submanifolds in unit Euclidean spheres. We also obtain some new results concerning geometric properties of proper biharmonic constant mean curvature…
The wave functions of a quantum isotropic harmonic oscillator in N-space modified by barriers at the coordinate hyperplanes can be expressed in terms of certain generalized spherical harmonics. These are associated with a product-type…
We formulate the statistics of peaks of non-Gaussian random fields and implement it to study the sphericity of peaks. For non-Gaussianity of the local type, we present a general formalism valid regardless of how large the deviation from…
In this paper we define spherical complexes as simplicial complexes with the property that every subcomplex obtained by a sequence of links and deletions either has trivial homology, or has the homology of a sphere. Examples of such…
The absence of interesting harmonic sections for the Sasaki and Cheeger-Gromoll metrics has led to the consideration of alternatives, for example in the form of a two-parameter family of natural metrics shown to relax existence conditions…
In this paper we study the asymptotic behavior of the angular bispectrum of spherical random fields. Here, the asymptotic theory is developed in the framework of fixed-radius fields, which are observed with increasing resolution as the…
This is Chapter 1 of the book {\it Approximation Theory and Harmonic Analysis on Spheres and Balls} by the authors. It provides a self-contained introduction to spherical harmonics. The book will be published as a title in {\it Springer…
We investigate horospherical homogeneous spaces--a class of spherical homogeneous spaces encompassing both flag varieties and algebraic tori--over fields of characteristic p>0, and establish their complete classification for p>2.
In this paper, we shall be concerned with geometric functionals and excursion probabilities for some nonlinear transforms evaluated on Fourier components of spherical random fields. In particular, we consider both random spherical harmonics…
This paper investigates the asymptotic behavior of structural break tests in the harmonic domain for time dependent spherical random fields. In particular, we prove a functional central limit theorem result for the fluctuations over time of…
In this paper, we describe a congruence property of solvable polynomials with coefficients in the Gaussian field Q(i).
Any homogeneous harmonic polynomial can be decomposed as a sum of powers of isotropic linear forms, that is, linear forms whose coefficients are the coordinates of isotropic points. The minimum size of such decompositions for a harmonic…
Matrix-valued covariance functions are crucial to geostatistical modeling of multivariate spatial data. The classical assumption of symmetry of a multivariate covariance function is overlay restrictive and has been considered as unrealistic…
We find that, in presence of the Snyder geometry, the quantization of d isotropic harmonic oscillators can be solved exactly.
We show how to express any Hasse-Schmidt derivation of an algebra in terms of a finite number of them under natural hypothesis. As an application, we obtain coefficient fields of the completion of a regular local ring of positive…
We study the growth of harmonic functions on complete Riemann-ian manifolds where the extrinsic diameter of geodesic spheres is sublinear. It is an generalization of a result of A. Kazue. We also get a Cheng and Yau estimates for the…