Gabor Szegö

A problem in prediction theory

SummaryA new kind of « prediction problem » is defined and studied, first for certain special distributions and then generally. The general results are connected with conjugate trigonometric series.

On a certain kind of symmetrization and its applications

SummaryA simple new method of symmetrization is defined and the change of various geometrical and physical quantities under this transformation investigated.

Determinants and Quadratic Forms

Interchanging two numbers in the numbering of the vertices is equivalent to the simultaneous interchange of two rows and two columns. If we give opposite vertices of the octahedron numbers that differ by 3, then the determinant

Functions of One Complex Variable Special Part

\left| {\begin{array}{*{20}c} 0 \hfill & 1 \hfill & 1 \hfill & 0 \hfill & 1 \hfill & 1 \hfill \\ 1 \hfill & 0 \hfill & 1 \hfill & 1 \hfill & 0 \hfill & 1 \hfill \\ 1 \hfill & 1 \hfill & 0 \hfill & 1 \hfill & 1 \hfill & 0 \hfill \\ 0 \hfill & 1 \hfill & 1 \hfill & 0 \hfill & 1 \hfill & 1 \hfill \\ 1 \hfill & 0 \hfill & 1 \hfill & 1 \hfill & 0 \hfill & 1 \hfill \\ 1 \hfill & 1 \hfill & 0 \hfill & 1 \hfill & 1 \hfill & 0 \hfill \\ \end{array} } \right| = 0.

The Integral as the Limit of a Sum of Rectangles

The power series

Mappings and Vector Fields

{a_1}z + {a_2}{z^2} + \cdots + {a_n}{z^n} + \cdots = \omega