Let M be an embedded cr manifold, p is an element of Gamma subset of M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{...
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Let M be an embedded cr manifold, p is an element of Gamma subset of M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\in \Gamma \subseteq M$$\end{document} such that Tp Gamma+J(Tp Gamma)=TpM+J(TpM)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_p\Gamma + J(T_p\Gamma )=T_pM+J(T_pM)$$\end{document}. If f=u+iv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f=u+iv$$\end{document} is a continuous cr function whose real part u satisfies |u(z)|<= aexp-b|z-p|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|u(z)|\le a\exp \left( \frac{-b}{|z-p|}\right) $$\end{document} for z is an element of Gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z\in \Gamma $$\end{document} and f vanishes to infinite order at p, then f vanishes on the cr orbit through p. If the exponential decay is satisfied by f itself, the result is due to Joricke (J Geom Anal 6(4):551-611, 1996).
We prove a generalization of a well-known theorem of Rado for continuous cr functions on a class of bihololomorphically invariant hypersurfaces that are considerably larger than convex ones of finite type and strictly...
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We prove a generalization of a well-known theorem of Rado for continuous cr functions on a class of bihololomorphically invariant hypersurfaces that are considerably larger than convex ones of finite type and strictly pseudoconvex hypersurfaces.
We study the geometric structure of the reproducing kernel Hilbert space associated to the continuous wavelet transform generated by the irreducible representations of the group of Euclidean motions of the plane SE(2)...
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We study the geometric structure of the reproducing kernel Hilbert space associated to the continuous wavelet transform generated by the irreducible representations of the group of Euclidean motions of the plane SE(2). A natural Hilbert norm for functions on the group is constructed that makes the wavelet transform an isometry, but since the considered representations are not square integrable, the resulting Hilbert space will not coincide with L-2(SE(2)). The reproducing kernel Hilbert subspace generated by the wavelet transform, for the case of a minimal uncertainty mother wavelet, can be characterized in terms of the complex regularity defined by the natural cr structure of the group. Relations with the Bargmann transform are presented.
We study an irreducible real-analytic germ of an n-dimensional variety in n dimensional complex space. Assuming that the variety is Segre nondegenerate we define an averaging operator that generalizes the Moser-Webste...
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We study an irreducible real-analytic germ of an n-dimensional variety in n dimensional complex space. Assuming that the variety is Segre nondegenerate we define an averaging operator that generalizes the Moser-Webster involution. This operator can be thought of as being the cr structure of the singularity, and using this operator we study the set of functions that are restrictions of holomorphic functions. We give a condition on the flattening of the singularity, that is realizing the singularity as a codimention one subvariety of a nonsingular Levi-flat hypersurface.
We show that for any smooth cr manifold which has a peak function (in a weak sense) at some point p, formal power series at p can be approximated asymptotically by continuous cr functions. Furthermore, if the peak fun...
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We show that for any smooth cr manifold which has a peak function (in a weak sense) at some point p, formal power series at p can be approximated asymptotically by continuous cr functions. Furthermore, if the peak function satisfies a certain growth property, the asymptotic approximation is actually smooth. This in fact allows to invert, in a Borel-type theorem, the natural map taking a smooth cr function to its formal Taylor series.
Let (X, (TX)-X-1,0) be a compact strongly pseudoconvex cr manifold of dimension 2n + 1. Assume that a d-dimensional torus T-d acts on X. In this work, we study the behavior of torus equivariant Szego & x30b;kernel...
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Let (X, (TX)-X-1,0) be a compact strongly pseudoconvex cr manifold of dimension 2n + 1. Assume that a d-dimensional torus T-d acts on X. In this work, we study the behavior of torus equivariant Szego & x30b;kernels and prove that the weighted torus equivariant Szego & x30b;kernels admit asymptotic expansions.
We introduce various notions of q-pseudo-concavity for abstract cr manifolds, and we apply these notions to the study of hypoellipticity, maximum modulus principle and Cauchy problems for cr functions.
We introduce various notions of q-pseudo-concavity for abstract cr manifolds, and we apply these notions to the study of hypoellipticity, maximum modulus principle and Cauchy problems for cr functions.
We discuss in Sect. 1 the property of regularity at the boundary of separately holomorphic functions along families of discs and apply, in Sect. 2, to two situations. First, let W be a wedge of C(n) with C(omega), gen...
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We discuss in Sect. 1 the property of regularity at the boundary of separately holomorphic functions along families of discs and apply, in Sect. 2, to two situations. First, let W be a wedge of C(n) with C(omega), generic edge E: a holomorphic function f on W has always a generalized (hyperfunction) boundary value bv(f) on E, and this coincides with the collection of the boundary values along the discs which have C(omega) transversal intersection with E. Thus Sect. 1 can be applied and yields the uniform continuity at E of f when bv(f) is (separately) continuous. When W is only smooth, an additional property, the temperateness of f at E, characterizes the existence of boundary value bv(f) as a distribution on E. If bv(f) is continuous, this operation is consistent with taking limits along discs (Theorem 2.8). By Sect. 1, this yields again the uniform continuity at E of tempered holomorphic functions with continuous bv. This is the theorem by Rosay (Trans. Am. Math. Soc. 297(1): 63-72, 1986), in whose original proof the method of "slicing" by discs is not used. As related literature we mention, among others, Sato et al. (Lecture Notes in Mathematics, vol. 287, pp. 265-529, Springer, Berlin, 1973), Komatsu (J. Fac. Sci., Univ. Tokyo Sect. IA, Math. 19: 201-214, 1972), Hormander (Grundlehren der mathematischen Wissenschaften, vol. 256, Springer-Verlag, Berlin, 1984), Cordaro and Treves (Annals of Mathematics Studies, vol. 136, Princeton University Press, Princeton, 1994), Baouendi et al. (Princeton Mathematical Series, Princeton University Press, Princeton, 1999) and Berhanu and Hounie (Math. Z. 255: 161-175, 2007).
It is known that a real analytic cr function f on a real analytic, generic submanifold M in C(N) can be holomorphically extended. A stronger result on a finite type, real analytic, generic submanifold M is found in wh...
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It is known that a real analytic cr function f on a real analytic, generic submanifold M in C(N) can be holomorphically extended. A stronger result on a finite type, real analytic, generic submanifold M is found in which we assume f a continuous cr function with real analytic imaginary part Im(f). The idea is contained in a general Schwarz reflection principle in one complex variable.
We study propagation of cr extendibility at the vertex p of an analytic sector A contained in a cr manifold M. Let k be the weighted vanishing order of M and the complex angle of A at p. Propagation takes place if and...
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We study propagation of cr extendibility at the vertex p of an analytic sector A contained in a cr manifold M. Let k be the weighted vanishing order of M and the complex angle of A at p. Propagation takes place if and only if alpha > 1/k. (C) 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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