n] be the vector space of

homogeneous polynomials on [C.

Equivariant cohomology [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] also has a Schubert basis indexed by Young diagrams, and the equivariant Littlewood-Richardson coefficients are

homogeneous polynomials in A = Z[[t.

j] = j(j + n - 1), j [greater than or equal to] 0 and the corresponding eigenfunctions, the so called spherical harmonics, are given as the restriction to the sphere of

homogeneous polynomials H([x.

j](u, v) are

homogeneous polynomials in (u, v) of degree j,j = 2, 3,.

i,[phi]], where each of the spaces Pi,[phi] contains only

homogeneous polynomials of degree i.

A

homogeneous polynomial (of degree n) P : A [right arrow] B is said to be orthogonally-additive if P(x + y) = P (x) + P (y) whenever x, y [member of] A are orthogonally (i.

TiSSEUR,Perturbation theory for

homogeneous polynomial eigenvalue problems, Linear Algebra Appl.

n]] consisting of

homogeneous polynomials P of degree d that are symmetric in [x.

v] be a

homogeneous polynomial of degree n, which is solution of (14) (here, the sums runs over sequences of non-negative integers of sum n).

n] converts each polynomial of the constant weight s into a polynomial of the constant weight s - 1 and each

homogeneous polynomial of degree d again into a

homogeneous polynomial of degree d.

It was shown by Kellogg [2] (see also [4]) that for every

homogeneous polynomial of degree m given by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

A

homogeneous polynomial [Mathematical Expressions Omitted] is called decomposable if it can be factorized into linear facotrs over some finite extension field G of K.

alpha]](x) is a

homogeneous polynomial of degree [absolute value of [alpha]].

p,q](x,z) is a

homogeneous polynomial of degree p + 2q except the two cases: [[bar.

1] is a

homogeneous polynomial of two variables, problem can be reduced to the two-dimensional case.