GENERALIZED FOURIER EXPANSIONS OF DIFFERENTIABLE FUNCTIONS ON THE SPHERE

Approximation on the Sphere by Weighted Fourier Expansions

A standard procedure to approximate a function f in an inner product space is to consider the Fourier series of the function with respect to an orthogonal system. The basic general results on this topic can be found in many references in the literature, for example, [2, Chapter VIII]. It is well known that even in the case in which K is a closed interval there always exists a function f in C(K)...

Fourier Expansions of Arithmetical Functions

Differentiable structures on the 7-sphere

The problem of classifying manifolds has always been central in geometry, and different categories of manifolds can a priori give different equivalence classes. The most famous classification problem of all times has probably been the Poincare’ conjecture, which asserts that every manifold which is homotopy equivalent to a sphere is actually homeomorphic to it. A large family of invariants have...

On the Fourier expansions of Jacobi forms

We use the relationship between Jacobi forms and vector-valued modular forms to study the Fourier expansions of Jacobi forms of indexes p, p2, and pq for distinct odd primes p, q. Specifically, we show that for such indexes, a Jacobi form is uniquely determined by one of the associated components of the vector-valued modular form. However, in the case of indexes of the form pq or p2, there are ...

gH-differentiable of the 2th-order functions interpolating

Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...