Zero-diminishing linear transformations

On Zero-Preserving Linear Transformations

For an arbitrary subset I of IR and for a function f defined on I, the number of zeros of f on I will be denoted by ZI(f) . In this paper we attempt to characterize all linear transformations T taking a linear subspace W of C(I) into functions defined on J (I, J ⊆ IR) such that ZI(f) = ZJ (Tf) for all f ∈ W .

A Zero–one Law for Linear Transformations of Lévy Noise

A Lévy noise on Rd assigns a random real “mass” Π(B) to each Borel subset B of Rd with finite Lebesgue measure. The distribution of Π(B) only depends on the Lebesgue measure of B, and if B1, . . . , Bn is a finite collection of pairwise disjoint sets, then the random variables Π(B1), . . . , Π(Bn) are independent with Π(B1 ∪ · · · ∪Bn) = Π(B1) + · · ·+ Π(Bn) almost surely. In particular, the di...

On fixed points of distance diminishing transformations on metric spaces

Linear Transformations

The n×m matrix AT obtained by exchanging rows and columns of A is called the transpose of A. A matrix A is said to be symmetric if A = AT . The sum of two matrices of equal size is the matrix of the entry-by-entry sums, and the scalar product of a real number a and an m× n matrix A is the m× n matrix of all the entries of A, each multiplied by a. The difference of two matrices of equal size A a...

On One-Sided Ideals of Rings of Linear Transformations