Uniform estimates for oscillatory integrals with homogeneous polynomial phases of degree 4

@article{Ruzhansky2022UniformEF,
  title={Uniform estimates for oscillatory integrals with homogeneous polynomial phases of degree 4},
  author={Michael Ruzhansky and A. R. Safarov and G. A. Khasanov},
  journal={Analysis and Mathematical Physics},
  year={2022},
  volume={12}
}
In this paper we consider the uniform estimates for oscillatory integrals with homogeneous polynomial phases of degree 4 in two variables. The obtained estimate is sharp and the result is an analogue of the more general theorem of Karpushkin (Proc I.G.Petrovsky Seminar 9:3–39, 1983) for sufficiently smooth functions, thus, in particular, removing the analyticity assumption. 
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References

SHOWING 1-10 OF 19 REFERENCES

On the growth and stability of real-analytic functions

This paper addresses the issue of whether integrals of real-analytic functions remain finite under small deformations. An approach based on uniform estimates for certain classes of one-dimensional…

INVARIANT ESTIMATES OF TWO-DIMENSIONAL TRIGONOMETRIC INTEGRALS

A uniform estimate is obtained for two-dimensional oscillating integrals with polynomial phase in terms of certain invariants of subgroups of affine groups. Bibliography: 22 titles.

Fourier Integrals in Classical Analysis

Background 1. Stationary phase 2. Non-homogeneous oscillatory integral operators 3. Pseudo-differential operators 4. The half-wave operator and functions of pseudo-differential operators 5. Lp…

Pointwise van der Corput Lemma for Functions of Several Variables ∗

A multidimensional version of the well-known van der Corput lemma is presented. A class of phase functions is described for which the corresponding oscillatory integrals satisfy a multidimensional…

Newton polyhedra and estimation of oscillating integrals

The aim of this paper is to calculate the principal term of the asymptotic expansion of an oscillating integral in a neighborhood of a singular critical point of the phase in terms of Newton's…

Uniform Estimates for the Fourier Transform of Surface Carried Measures in ℝ3 and an Application to Fourier Restriction

AbstractLet S be a hypersurface in ${\Bbb{R}}^{3}$ which is the graph of a smooth, finite type function φ, and let μ=ρ  dσ be a surface carried measure on S, where dσ denotes the surface element on…

Multidimensional decay in van der Corput lemma

In this paper we present a multidimensional version of the van der Corput lemma where the decay of the oscillatory integral is gained with respect to all space variables, connecting the standard…

Harmonic analysis

  • Vladimir I. Clue
  • Engineering
    2004 IEEE Electro/Information Technology Conference
  • 2004
A method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms, of a signal having an arbitrary dimension of the digital representation by reducing the transform to a vector-to-circulant matrix multiplying.

Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra

This is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all…

Singularities of differentiable maps

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