Results 41 to 50 of about 10,275,715 (164)
Higher-order Pseudoconvex Functions
, 2007 In terms of n-th order Dini directional derivative with n positive integer we define n-pseudoconvex functions being a generalization of the usual pseudoconvex functions. Again with the n-th order Dini derivative we define n-stationary points, and prove that a point x 0 is a global minimizer of a n-pseudoconvex function f if and only if x 0 is a n ...
Ivan Ginchev, Vsevolod I. Ivanov
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On a higher dimensional worm domain and its geometric properties
Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.Abstract We construct new three‐dimensional variants of the classical Diederich–Fornæss worm domain. We show that they are smoothly bounded, pseudoconvex, and have nontrivial Nebenhülle. We also show that their Bergman projections do not preserve the Sobolev space for sufficiently large Sobolev indices.
Steven G. Krantz +2 more
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Szegö kernel asymptotic expansion on strongly pseudoconvex CR manifolds with S1 action [PDF]
International Journal of Mathematics, 2016 Let [Formula: see text] be a compact connected strongly pseudoconvex Cauchy–Riemann (CR) manifold of real dimension [Formula: see text] with a transversal CR [Formula: see text] action on [Formula: see text]. We establish an asymptotic expansion for the [
H. Herrmann, Chin-Yu Hsiao, Xiaoshan Li
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Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.Abstract Using iterated uniform local completion, we introduce a notion of continuous CR$CR$ functions on locally closed subsets of reduced complex spaces, generalising both holomorphic functions and CR$CR$ functions on CR$CR$ submanifolds. Under additional assumptions of set‐theoretical weak pseudo‐concavity, we prove optimal maximum modulus ...
Mauro Nacinovich, Egmont Porten
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On Carleman and observability estimates for wave equations on time‐dependent domains
Proceedings of the London Mathematical Society, Volume 119, Issue 4, Page 998-1064, October 2019., 2019 Abstract We establish new Carleman estimates for the wave equation, which we then apply to derive novel observability inequalities for a general class of linear wave equations. The main features of these inequalities are that (a) they apply to a fully general class of time‐dependent domains, with timelike moving boundaries, (b) they apply to linear ...
Arick Shao
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A note on quasiconvex functions that are pseudoconvex
Trabajos de Investigacion Operativa, 1987 The author considers the class of locally pseudo-convex functions and the class of locally quasi-convex functions at a point \(x^ 0\in X\subseteq \mathbb R^ n\), both following the definitions of \textit{O. L. Mangasarian} [``Nonlinear programming.'' New York etc.: McGraw-Hill (1969; Zbl 0194.20201)] and \textit{B.
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Estimates for derivatives of holomorphic functions in pseudoconvex domains [PDF]
Mathematische Zeitschrift, 1986 Let D be a strictly pseudoconvex domain and let M be the intersection with D of a submanifold of a neighborhood of D which intersect bd(D) transversally. Let f be a holomorphic function on M lying in some \(L^ p\) class. An interesting problem is to find a holomorphic extension of f to D satisfying some optimal \(L^ p\) estimate.
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An exotic calculus of Berezin–Toeplitz operators
Mathematika, Volume 71, Issue 2, April 2025.Abstract We develop a calculus of Berezin–Toeplitz operators quantizing exotic classes of smooth functions on compact Kähler manifolds and acting on holomorphic sections of powers of positive line bundles. These functions (classical observables) are exotic in the sense that their derivatives are allowed to grow in ways controlled by local geometry and ...
Izak Oltman
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Criterion for Generalized Weakly Fuzzy Invex Monotonocities
Advances in Fuzzy Systems, Volume 2018, Issue 1, 2018., 2018 The present paper deals with the concepts of generalized fuzzy invex monotonocities and generalized weakly fuzzy invex functions. Some necessary conditions for weakly fuzzy invex monotonocities are presented. Moreover, the concept of fuzzy strong invex monotonocities and fuzzy strong invex functions are also discussed. To strengthen our definitions, we
Meraj A. Khan +3 more
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Extension of holomorphic functions defined on singular complex hypersurfaces with growth estimates in strictly pseudoconvex domains of $\mathbb{C}^n$ [PDF]
Annales Polonici Mathematici, 2018 Let D be a strictly convex domain and X be a singular complex hypersurface in Cn such that X \ D 6= ; and X \ bD is transverse. We first give necessary conditions for a function holomorphic on D\X to admit a holomorphic extension belonging to Lq (D ...
William Alexandre, E. Mazzilli
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