On the Hilbert-Samuel polynomial in complex analytic geometry

On Bernstein Type Inequalities for Complex Polynomial

In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.

Composition operators acting on weighted Hilbert spaces of analytic functions

In this paper, we considered composition operators on weighted Hilbert spaces of analytic functions and  observed that a formula for the  essential norm, gives a Hilbert-Schmidt characterization and characterizes the membership in Schatten-class for these operators. Also, closed range composition operators  are investigated.

On Balls in a Hilbert Polygonal Geometry

Hilbert geometry is a metric geometry that extends the hyperbolic Cayley-Klein geometry. In this video, we explain the shape of balls and their properties in a convex polygonal Hilbert geometry. First, we study the combinatorial properties of Hilbert balls, showing that the shapes of Hilbert polygonal balls depend both on the center location and on the complexity of the Hilbert domain but not o...

An algorithm for the Hilbert - Samuel function of a primary

The Hilbert Polynomial and Degree

Proof. The first assertion is Exercise III.5.2 of [1]. The degree assertion can be deduced by modifying the proof of the same exercise to remove the first term of the exact sequence, using Corollary 4.1 of [2] (and noting that invariance of cohomology under field extension means we can reduce immediately to the case of an infinite field). The last equality follows from Serre’s theorem on vanish...