Newton polyhedra and estimation of oscillating integrals

DOI10.1007/BF01075524zbMath0351.32011OpenAlexW2072778147WikidataQ56593977 ScholiaQ56593977MaRDI QIDQ1235300

Publication date: 1977

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01075524

Mathematics Subject Classification ID

Germs of analytic sets, local parametrization (32B10) (C^infty)-functions, quasi-analytic functions (26E10) Critical points and critical submanifolds in differential topology (57R70) Complex singularities (32Sxx) Polytopes and polyhedra (52Bxx)

Related Items (92)

Une estimation asymptotique du nombre de solutions approchées d'une équation p-adique. (Asymptotic estimation of the number of approximate solutions of a p-adic equation) ⋮ A direct resolution of singularities for functions of two variables with applications to analysis ⋮ $L^2$ Estimates of trilinear oscillatory integrals of convolution type on $\mathbb{R}^2$ ⋮ On Meromorphic Continuation of Local Zeta Functions ⋮ Parameter dependence of the Bergman kernels ⋮ On the volume and the number of lattice points of some semialgebraic sets ⋮ The asymptotic behavior of degenerate oscillatory integrals in two dimensions ⋮ Applications of an elementary resolution of singularities algorithm to exponential sums and congruences modulo $p^n$ ⋮ Asymptotic analysis of oscillatory integrals via the Newton polyhedra of the phase and the amplitude ⋮ Fourier inversion of distributions supported by a hypersurface ⋮ On the $\alpha $-invariants of cubic surfaces with Eckardt points ⋮ Integration of oscillatory and subanalytic functions ⋮ Punctures and $p$-spin curves from matrix models. III: $D_l$ type and logarithmic potential ⋮ Spectral estimates around a critical level ⋮ Local zeta function for curves, non-degeneracy conditions and Newton polygons ⋮ Local zeta functions and Newton polyhedra ⋮ A fast algorithm for curve singularities ⋮ Unnamed Item ⋮ The Klein-Gordon equation on $\mathbb Z^2$ and the quantum harmonic lattice ⋮ Topologically Principal Part of Analytic Functions ⋮ Improved Hörmander's theorem and new methods for oscillatory integral operators ⋮ Sharp $L^{p}$-boundedness of oscillatory integral operators with polynomial phases ⋮ Meromorphic continuations of local zeta functions and their applications to oscillating integrals ⋮ Mixed norm Strichartz-type estimates for hypersurfaces in three dimensions ⋮ Oscillatory integral operators with homogeneous polynomial phases in several variables ⋮ Multiple Hilbert transforms associated with polynomials ⋮ Singularities of rational inner functions in higher dimensions ⋮ Resolution of singularities in two dimensions and the stability of integrals ⋮ Continuum limit of 2D fractional nonlinear Schrödinger equation ⋮ Strichartz estimates for mixed homogeneous surfaces in three dimensions ⋮ Sharp $L^p$ decay estimates for degenerate and singular oscillatory integral operators ⋮ Resolution of singularities for $C^\infty$ functions and meromorphy of local zeta functions ⋮ Sublevel-set estimates over global domains ⋮ Newton polygon and distribution of integer points in sublevel sets ⋮ Reconstructions of the asymptotics of an integral determined by a hyperbolic unimodal singularity ⋮ Resolution of singularities, asymptotic expansions of integrals and related phenomena ⋮ Unnamed Item ⋮ A sharp decay estimate for degenerate oscillatory integral operators using broad-narrow method ⋮ On estimates for maximal operators ⋮ Lifshitz tails for 2-dimensional random Schrödinger operators. ⋮ Minimal characteristic exponent of the Gauss-Manin connexion of an isolated singular point and Newton polyhedron ⋮ $L^{p}$ Sobolev regularity of averaging operators over hypersurfaces and the Newton polyhedron ⋮ Asymptotics of multivariate sequences. III: Quadratic points ⋮ Smooth and singular maximal averages over 2D hypersurfaces and associated Radon transforms ⋮ An estimate of approximation constants for $p$-adic and real varieties ⋮ Stability of oscillatory integral asymptotics in two dimensions ⋮ On some generalizations of Jacobi's residue formula ⋮ Sharp Bounds for Oscillatory Integral Operators with Homogeneous Polynomial Phases ⋮ Newton polygons and local integrability of negative powers of smooth functions in the plane ⋮ Unnamed Item ⋮ On adapted coordinate systems ⋮ The Newton polyhedron and positivity of $_2F_3$ hypergeometric functions ⋮ Fourier transforms of powers of well-behaved 2D real analytic functions ⋮ Periods and the asymptotics of a diophantine problem. I ⋮ Newton polyhedra and order of contact on real hypersurfaces ⋮ An elementary coordinate-dependent local resolution of singularities and applications ⋮ Newton polyhedron and $f^ s_ +$ distribution. II ⋮ $L^p$ Sobolev regularity for a class of Radon and Radon-like transforms of various codimension ⋮ The modified analytic trivialization of family of real analytic functions ⋮ Oscillatory integral decay, sublevel set growth, and the Newton polyhedron ⋮ 2-dimensional localization of acoustic waves in random perturbation of periodic media ⋮ Zeta functions for analytic mappings, log-principalization of ideals, and Newton polyhedra ⋮ Hyperplane integrability conditions and smoothing for Radon transforms ⋮ Newton polyhedra and weighted oscillatory integrals with smooth phases ⋮ Uniform bounds for Fourier transforms of surface measures in R$^3$ with nonsmooth density ⋮ Meromorphy of local zeta functions in smooth model cases ⋮ Fourier transforms of indicator functions, lattice point discrepancy, and the stability of integrals ⋮ Singular integral operators with kernels associated to negative powers of real-analytic functions ⋮ Unnamed Item ⋮ Decay rates of oscillatory integral operators in “1 + 2” dimensions ⋮ Residue currents constructed from resolutions of monomial ideals ⋮ Estimation of Lojasiewicz exponents and Newton polygons ⋮ Maximal averages over hypersurfaces and the Newton polyhedron ⋮ Damping estimates for oscillatory integral operators with real-analytic phases and its applications ⋮ A survey on oscillatory integral operators ⋮ Finite Trotter approximation to the averaged mean square distance in the Anderson model ⋮ Uniform resolvent estimates for the discrete Schrödinger operator in dimension three ⋮ Oscillating integrals and Newton polyhedra ⋮ Uniform estimates for oscillatory integrals with homogeneous polynomial phases of degree 4 ⋮ Stationary points at infinity for analytic combinatorics ⋮ Unnamed Item ⋮ Fourier transform of surface-carried measures of two-dimensional generic surfaces and applications ⋮ An estimate of the roots of b-functions by Newton polyhedra ⋮ Morse Theory, Stratifications and Sheaves ⋮ Newton polyhedra and Igusa's local zeta function ⋮ A regularization of Dirac delta function for a singular analytic function ⋮ Lifshitz tails for random perturbations of periodic Schrödinger operators ⋮ Pre-weighted homogeneous map germs—Finite determinacy and topological triviality ⋮ A semi-classical trace formula for several commuting operators ⋮ Damping oscillatory integrals ⋮ Séries de Dirichlet et intégrales associées à un polynôme à deux indéterminées. (Dirichlet series and integrals associated with a polynomial of two variables) ⋮ Weighted inequalities for real-analytic functions in $\mathbb R^ 2$.

Cites Work

This page was built for publication: Newton polyhedra and estimation of oscillating integrals