Newton polyhedra and weighted oscillatory integrals with smooth phases

DOI10.1090/tran/6528zbMath1335.58025arXiv1406.4325OpenAlexW1656505307MaRDI QIDQ2790695

Toshihiro Nose, Joe Kamimoto

Publication date: 8 March 2016

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.4325

zbMATH Keywords

resolution of singularitiesNewton polyhedronNewton distanceoscillation index and its multiplicityNewton multiplicityprincipal facesweighted oscillatory integrals

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Asymptotic behavior of solutions to equations on manifolds (58K55)

Related Items (8)

On Archimedean zeta functions and Newton polyhedra ⋮ Some oscillatory integral estimates via real analysis ⋮ Archimedean zeta functions and oscillatory integrals ⋮ Integrability at infinity of negative powers of polynomials in the plane and its application to convergence of Dirichlet series ⋮ Resolution of singularities for \(C^\infty\) functions and meromorphy of local zeta functions ⋮ Newton polyhedra and order of contact on real hypersurfaces ⋮ Meromorphy of local zeta functions in smooth model cases ⋮ Nonpolar singularities of local zeta functions in some smooth case

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Meromorphic continuations of local zeta functions and their applications to oscillating integrals
• Estimates for maximal functions associated with hypersurfaces in \(\mathbb R^3\) and related problems of harmonic analysis
• Resolution of singularities, asymptotic expansions of integrals and related phenomena
• Uniform estimates for the Fourier transform of surface carried measures in \(\mathbb R^{3}\) and an application to Fourier restriction
• Lectures on forms of higher degree. Notes by S. Raghavan
• The asymptotic behavior of degenerate oscillatory integrals in two dimensions
• Asymptotic behavior of exponential integrals in the complex domain
• Newton polyhedra and estimation of oscillating integrals
• Maximal averages over surfaces
• The Newton polyhedron and oscillatory integral operators
• Resolution of singularities in Denjoy-Carleman classes
• Oscillatory integral decay, sublevel set growth, and the Newton polyhedron
• Asymptotic analysis of oscillatory integrals via the Newton polyhedra of the phase and the amplitude
• On quasianalytic local rings
• Meromorphic property of the functions \(P^ \lambda\)
• Oscillating integrals and Newton polyhedra
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• A multi-dimensional resolution of singularities with applications to analysis
• On adapted coordinate systems
• Introduction to Toric Varieties. (AM-131)
• Intégrales asymptotiques et monodromie
• Lectures on Polytopes
• Decay estimates for weighted oscillatory integrals in R^2
• Toric resolution of singularities in a certain class of $C^{\infty}$ functions and asymptotic analysis of oscillatory integrals
• Resolution of Singularities and Division of Distributions

This page was built for publication: Newton polyhedra and weighted oscillatory integrals with smooth phases