Morera conditions along real planes and a characterization of CR functions on boundaries of domains in CN.
Morera theorem for holomorphic Hp spaces in the Heisenberg group.
Morphisme cellulaire et classes de Chern bivariantes
Morphismes surjectifs de fibrés vectoriels semi-positifs
Morphisms of projective varieties from the viewpoint of minimal model theory [Book]
Motivic-type invariants of blow-analytic equivalence
To a given analytic function germ , we associate zeta functions , , defined analogously to the motivic zeta functions of Denef and Loeser. We show that our zeta functions are rational and that they are invariants of the blow-analytic equivalence in the sense of Kuo. Then we use them together with the Fukui invariant to classify the blow-analytic equivalence classes of Brieskorn polynomials of two variables. Except special series of singularities our method classifies as well the blow-analytic...
Multidimensional analogue of the van der Corput-Visser inequality and its application to the estimation of the Bohr radius
We present a multidimensional analogue of an inequality by van der Corput-Visser concerning the coefficients of a real trigonometric polynomial. As an application, we obtain an improved estimate from below of the Bohr radius for the hypercone 𝓓₁ⁿ = {z ∈ ℂⁿ: |z₁|+. .. +|zₙ| < 1} when 3 ≤ n ≤ 10.
Multidimensional residues and ideal membership.
Let I(f) be a zero-dimensional ideal in C[z1, ..., zn] defined by a mapping f. We compute the logarithmic residue of a polynomial g with respect to f. We adapt an idea introduced by Aizenberg to reduce the computation to a special case by means of a limiting process.We then consider the total sum of local residues of g w.r.t. f. If the zeroes of f are simple, this sum can be computed from a finite number of logarithmic residues. In the general case, you have to perturb the mapping f. Some applications...
Multifonctions analytiques polygonales
Multiple fibres of a morphism.
Multiple Laurent series and difference equations.
Multiple values and uniqueness problem for meromorphic mappings sharing hyperplanes
The purpose of this article is to deal with multiple values and the uniqueness problem for meromorphic mappings from into the complex projective space ℙⁿ(ℂ) sharing hyperplanes. We obtain two uniqueness theorems which improve and extend some known results.
Multiple zeta values and periods of moduli spaces
We prove a conjecture due to Goncharov and Manin which states that the periods of the moduli spaces of Riemann spheres with marked points are multiple zeta values. We do this by introducing a differential algebra of multiple polylogarithms on and proving that it is closed under the operation of taking primitives. The main idea is to apply a version of Stokes’ formula iteratively to reduce each period integral to multiple zeta values. We also give a geometric interpretation of the double shuffle...
Multiplicative isometries on the Smirnov class
We show that T is a surjective multiplicative (but not necessarily linear) isometry from the Smirnov class on the open unit disk, the ball, or the polydisk onto itself, if and only if there exists a holomorphic automorphism Φ such that T(f)=f ○ Φ for every class element f or T(f) = for every class element f, where the automorphism Φ is a unitary transformation in the case of the ball and Φ(z 1, ..., z n) = for |λ j| = 1, 1 ≤ j ≤ n, and (i 1; ..., i n)is some permutation of the integers from...
Multiplicative linear functionals on some algebras of holomorphic functions with restricted growth
Multiplicieties and equisingularity of ICIS germs.
Multiplicity and the Lojasiewicz exponent
Multiplicity and the Łojasiewicz exponent
We give a formula for the multiplicity of a holomorphic mapping , m > n, at an isolated zero, in terms of the degree of an analytic set at a point and the degree of a branched covering. We show that calculations of this multiplicity can be reduced to the case when m = n. We obtain an analogous result for the local Łojasiewicz exponent.
Multiplicity of polynomials on trajectories of polynomial vector fields in
Let ξ be a polynomial vector field on with coefficients of degree d and P be a polynomial of degree p. We are interested in bounding the multiplicity of a zero of a restriction of P to a non-singular trajectory of ξ, when P does not vanish identically on this trajectory. Bounds doubly exponential in terms of n are already known ([9,5,10]). In this paper, we prove that, when n=3, there is a bound of the form . In Control Theory, such a bound can be used to give an estimate of the degree of nonholonomy...
Multiplicity-free complex manifolds.