Dunham Jackson
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View article: The boundedness of certain sets of orthonormal polynomials in one, two, and three variables
The boundedness of certain sets of orthonormal polynomials in one, two, and three variables Open
September 2. The curves y = x3, y=xm; permutation of powers of x.In connection with the curve y = x2 it has been pointed out [7, p. 361] that the independent monomials for the application of the Schmidt process may be taken as 1. *. y, xy,…
View article: Bernstein’s theorem and trigonometric approximation
Bernstein’s theorem and trigonometric approximation Open
couronné, Brussels, 1912, p. 20 (with 2nL instead of nL as upper bound for I Tn M|)> M. Riesz, Eine trigonometrische Interpolationsformel und einige Ungleichungen für Poly-
View article: The summation of series of orthogonal polynomials
The summation of series of orthogonal polynomials Open
measure zero is immaterial.
View article: Certain problems of closest approximation
Certain problems of closest approximation Open
The words "of the nth order" or "of the nth degree" will be understood throughout to mean of the nth order or of the nth degree at most.* See also D. Jackson, Orthogonal trigonometric sums, presently to be published in the Annals of Mathem…
View article: The geometry of frequency functions
The geometry of frequency functions Open
The fundamental idea of attaching a geometric meaning to the correlation coefficient appears to be due to Pearson himself.* Cf. the papers on The trigonometry of correlation and The elementary geometry of function space, previously cited.
View article: A Generalized Problem in Weighted Approximation
A Generalized Problem in Weighted Approximation Open
This will be understood throughout to mean a trigonometric sum of order n at most.
View article: A symmetric coefficient of correlation for several variables
A symmetric coefficient of correlation for several variables Open
Let (x v x v • • •, x^j and {y v y 2 , • •• •, j/ w ) be two sets of n real numbers each, neither set consisting entirely of zeros.In order that the ensuing use of technical terms may be in accordance with established practice, let it be s…
View article: On Approximation by Functions of Given Continuity
On Approximation by Functions of Given Continuity Open
Somewhat more directly, the existence of a minimum follows almost immediately from a well known theorem in the theory of functions of lines.* When the approximating function is not unique, ^ may be any approximating function corresponding …
View article: Note on an ambiguous case of approximation
Note on an ambiguous case of approximation Open
shall have the smallest possible value, n being a given positive integer (or zero) and m a given number ? 1, not necessarily integral.t The purpose of the present note is to inquire what becomes of the problem for values of m less than 1. …
View article: Note on a Class of Polynomials of Approximation
Note on a Class of Polynomials of Approximation Open
The main problem of the paper cited, going somewhat beyond the result quoted here, had previously been treated, for the polynomial case, by Pólya, in a note with which I was not acquainted at the time of writing: