A Blaschke sequence that is not a zero set for $\ell ^p_A$

Raymond Cheng; James G. Dragas

doi:10.1090/proc/14548

A Blaschke sequence that is not a zero set for $\ell ^p_A$

Proceedings of the American Mathematical Society ◽

10.1090/proc/14548 ◽

2019 ◽

Vol 147 (9) ◽

pp. 3927-3936 ◽

Cited By ~ 1

Author(s):

Raymond Cheng ◽

James G. Dragas

Keyword(s):

Zero Set

Download Full-text

Functions in the Schwartz algebra that are invertible in the sense of Ehrenpreis

Доклады Академии наук ◽

10.31857/s0869-565248417-11 ◽

2019 ◽

Vol 484 (1) ◽

pp. 7-11

Author(s):

N. F. Abuzyarova

Keyword(s):

Entire Function ◽

Exponential Type ◽

Zero Set ◽

Schwartz Algebra

We consider the problem of obtaining the restrictions on the zero set of an entire function of exponential type under which this function belongs to the Schwartz algebra and invertible in the sense of Ehrenpreis.

Download Full-text

A note on extensions of multilinear maps defined on multilinear varieties

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091521000055 ◽

2021 ◽

pp. 1-26

Author(s):

W. T. Gowers ◽

L. Milićević

Keyword(s):

Finite Fields ◽

Vector Spaces ◽

Restriction Map ◽

Zero Set ◽

Dimensional Vector ◽

Prime Field ◽

Finite Dimensional ◽

Multilinear Maps ◽

Multilinear Map

Abstract Let $G_1, \ldots , G_k$ be finite-dimensional vector spaces over a prime field $\mathbb {F}_p$ . A multilinear variety of codimension at most $d$ is a subset of $G_1 \times \cdots \times G_k$ defined as the zero set of $d$ forms, each of which is multilinear on some subset of the coordinates. A map $\phi$ defined on a multilinear variety $B$ is multilinear if for each coordinate $c$ and all choices of $x_i \in G_i$ , $i\not =c$ , the restriction map $y \mapsto \phi (x_1, \ldots , x_{c-1}, y, x_{c+1}, \ldots , x_k)$ is linear where defined. In this note, we show that a multilinear map defined on a multilinear variety of codimension at most $d$ coincides on a multilinear variety of codimension $O_{k}(d^{O_{k}(1)})$ with a multilinear map defined on the whole of $G_1\times \cdots \times G_k$ . Additionally, in the case of general finite fields, we deduce similar (but slightly weaker) results.

Download Full-text