Bernstein polynomials and spectral numbers for linear free divisors

Linear Free Divisors

A free divisor D in C is linear if its module of logarithmic vector fields has a basis of global vector fields of degree 0. It is then defined by a homogeneous polynomial of degree n and its complement is an open orbit of an algebraic subgroup GD in Gln(C). The best known example is the normal crossing divisor. Many other such divisors arise, for instance, from quiver representations. We give a...

A Pointwise Approximation Theorem for Linear Combinations of Bernstein Polynomials

Recently, Z. Ditzian gave an interesting direct estimate for Bernstein polynomials. In this paper we give direct and inverse results of this type for linear combinations of Bernstein polynomials.

Some Identities on the Twisted (h, q)-Genocchi Numbers and Polynomials Associated with q-Bernstein Polynomials

Let p be a fixed odd prime number. Throughout this paper, we always make use of the following notations: Z denotes the ring of rational integers, Zp denotes the ring of padic rational integer, Qp denotes the ring of p-adic rational numbers, and Cp denotes the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers and Z N {0}. Let Cpn {ζ | ζpn 1} be the cyclic g...

Some Identities of Bernoulli Numbers and Polynomials Associated with Bernstein Polynomials

On the Fermionic p-adic Integral Representation of Bernstein Polynomials Associated with Euler Numbers and Polynomials

Throughout this paper, let p be an odd prime number. The symbol, p, p , and p denote the ring of p-adic integers, the field of p-adic rational numbers, the complex number field and the completion of algebraic closure of p , respectively. Let be the set of natural numbers and ∪ {0}. Let νp be the normalized exponential valuation of p with |p|p p−νp p 1/p. Note that p {x | |x|p ≤ 1} lim← N /p p. ...