scholarly journals Newton Polyhedra and Good Compactification Theorem

2020 ◽  
Author(s):  
Askold Khovanskii
Keyword(s):  
Newton Polyhedra

Exponential Sums and Newton Polyhedra: Cohomology and Estimates

1989 ◽  
Vol 130 (2) ◽  
pp. 367 ◽  
Author(s):  
Alan Adolphson ◽  
Steven Sperber
Keyword(s):  
Exponential Sums ◽  
Newton Polyhedra

Asymptotics and Newton polyhedra

1988 ◽  
pp. 233-262
Author(s):  
V. I. Arnold ◽  
S. M. Gusein-Zade ◽  
A. N. Varchenko
Keyword(s):  
Newton Polyhedra

Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in R3, and Newton Polyhedra Detlef Müller

2014 ◽  
Keyword(s):  
Harmonic Analysis ◽  
Finite Type ◽  
Maximal Function ◽  
Oscillatory Integrals ◽  
The Other ◽  
Riemannian Surface ◽  
Fourier Restriction ◽  
Newton Polyhedra ◽  
The Given ◽  
Finite Type Hypersurfaces

This chapter presents three sets of problems and explains how these questions can be answered in an (almost) complete way in terms of Newton polyhedra associated to the given surface S (here, a smooth, finite type hypersurface in R³ with Riemannian surface measure dσ‎). The first problem is a classical question about estimates for oscillatory integrals, and there exists a huge body of results on it, in particular for convex hypersurfaces. The other two problems had first been formulated by Stein: the study of maximal averages along hypersurfaces has been initiated in Stein's work on the spherical maximal function, and also the idea of Fourier restriction goes back to him.

Newton filtrations, graded algebras and codimension of non-degenerate ideals

2002 ◽  
Vol 133 (1) ◽  
pp. 55-75 ◽  
Author(s):  
CARLES BIVIÀ-AUSINA ◽  
TOSHIZUMI FUKUI ◽  
MARCELO JOSÉ SAIA
Keyword(s):  
Graded Algebras ◽  
Newton Polyhedra ◽  
Degeneracy Condition

We investigate a generalization of the method introduced by Kouchnirenko to compute the codimension (colength) of an ideal under a certain non-degeneracy condition on a given system of generators of I. We also discuss Newton non-degenerate ideals and give characterizations using the notion of reductions and Newton polyhedra of ideals.

Newton polyhedra and irreducibility

1988 ◽  
Vol 199 (1) ◽  
pp. 119-127 ◽  
Author(s):  
Aleksandar Lipkovski
Keyword(s):  
Newton Polyhedra
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