论文信息 - Certain Hilbert spaces of entire functions

Certain Hilbert spaces of entire functions

1. Introduction. The research reported on in the present note was motivated by the following Proposition (F), due to Ernest Fischer ([5], see also [4] for an earlier version; actually Fischer proved a more general result, but the special case suffices as a point of departure for our discussion) : (F) Let P denote a homogeneous polynomial in si, • • • , z k with complex coefficients. Then every polynomial in Si, • • • , z k has a unique representation QP+R where

Harold S. Shapiro | Donald J. Newman | D. Newman | H. Shapiro

[1] Harold S. Shapiro,et al. The level curves of harmonic functions , 1966 .

[2] V. Bargmann. On a Hilbert space of analytic functions and an associated integral transform part I , 1961 .

[3] J. F. Treves. Lectures on linear partial differential equations with constant coefficients , 1961 .

[4] B. Malgrange. Sur une inégalité de F. Treves , 1959 .

[5] J. Horváth. Basic sets of polynomial solutions for partial differential equations. , 1958 .

[6] B. Malgrange. Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution , 1956 .

[7] E. Hobson. The Theory of Spherical and Ellipsoidal Harmonics , 1955 .

[8] L. Ehrenpreis. Mean Periodic Functions: Part I. Varieties Whose Annihilator Ideals Are Principal , 1955 .

[9] H. Muggli. Differentialgleichungen unendlich hoher Ordnung , 1941 .

[10] G. Valiron. Sur les solutions des équations différentielles linéaires d'ordre infini et à coefficients constants , 1929 .

[11] E. Fischer. Über algebraische Modulsysteme und lineare homogene partielle Differentialgleichungen mit konstanten Koeffizienten. , 1911 .