j] (x,y,[alpha]) are

homogeneous polynomials in (x,y,[alpha]) of degree j(j = 2, 3,.

Let A and B be vector lattices, let P: A [right arrow] B be a

homogeneous polynomial of degree n and let [PSI] : [A.

k] is a

homogeneous polynomial of degree k with integral coefficients and of weight k in the variables [b.

Given a decomposable

homogeneous polynomial F([[functions of x].

In this note we obtain an asymptotically sharp Remez-type inequality for

homogeneous polynomials on the unit sphere in [R.

3) with p a

homogeneous polynomial is homogeneous with respect to a nonisotropic group of dilations (see Section 1).

n]), is a

homogeneous polynomial of total degree d over k, a finite field having q = [p.

An

homogeneous polynomial f(X) is said to be diagonally W, q-harmonic (or q-harmonic for short) if

LAMBDA]] is a

homogeneous polynomial attached to [LAMBDA], determined by the geometry of the discriminant hypersurface of W (see Sec.

the algebra of polynomial functions on V generated by

homogeneous polynomial functions of degree q.

GFs as defined are a generalization of (and contain) the (classical) forms, which are

homogeneous polynomials consisting of monomials, which are products of terms [x.

Specific topics include stable expansions in

homogeneous polynomials, Schottky's theorem on comformal mappings between annuli, Univalent convex functions in the positive direction of the real axis, controlled approximation for some classes of homomorphic functions, connected complex orbits, the QC Reimann mapping theorem in space, analytic properties of Besov spaces via Bergman projections, analytic functions in algebras, quadratic forms in geometric function theory (including quasi-conformal extensions and Fredhom eigenvalues), the Cauchy problem of couple-stress elasticity, mappings associated with weighted Sobolev spaces, the parabolicity of minimal groups, and harmonic polynomial interpolation.