Sectorial extensions, via Laplace transforms, in ultraholomorphic classes defined by weight functions

DOI10.1007/s00025-018-0951-1zbMath1419.46020arXiv1710.10081OpenAlexW3101880150WikidataQ128595539 ScholiaQ128595539MaRDI QIDQ667536

Javier Sanz, Javier Jiménez-Garrido, Gerhard Schindl

Publication date: 28 February 2019

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.10081

zbMATH Keywords

Laplace transformweight sequencesextension operatorscontinuous right-inversefunctions and matricesindices of O-regular variationLegendre conjugatesultraholomorphic classes

Mathematics Subject Classification ID

Moment problems and interpolation problems in the complex plane (30E05) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Topological linear spaces of continuous, differentiable or analytic functions (46E10) Rate of growth of functions, orders of infinity, slowly varying functions (26A12) General integral transforms (44A05)

Related Items (19)

Equality of ultradifferentiable classes by means of indices of mixed O-regular variation ⋮ Some notes on moment partial differential equations. Application to fractional functional equations ⋮ On subadditivity-like conditions for associated weight functions ⋮ The theorem of iterates for elliptic and non-elliptic operators ⋮ On optimal solutions of the Borel problem in the Roumieu case ⋮ Sectorial extensions for ultraholomorphic classes defined by weight functions ⋮ The Borel map in the mixed Beurling setting ⋮ On generalized definitions of ultradifferentiable classes ⋮ Ultraholomorphic extension theorems in the mixed setting ⋮ On inclusion relations between weighted spaces of entire functions ⋮ Unnamed Item ⋮ Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting ⋮ Sectorial extensions, via Laplace transforms, in ultraholomorphic classes defined by weight functions ⋮ Ultraholomorphic sectorial extensions of Beurling type ⋮ On the extension of Whitney ultrajets of Beurling type ⋮ The surjectivity of the Borel mapping in the mixed setting for ultradifferentiable ramification spaces ⋮ On the construction of large algebras not contained in the image of the Borel map ⋮ Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis ⋮ Indices of O-regular variation for weight functions and weight sequences

Cites Work

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• Strongly regular sequences and proximate orders
• Sectorial extensions, via Laplace transforms, in ultraholomorphic classes defined by weight functions
• Continuous right inverses for the asymptotic Borel map in ultraholomorphic classes via a Laplace-type transform
• Log-convex sequences and nonzero proximate orders
• Smooth solutions of quasianalytic or ultraholomorphic equations
• Almost analytic extension of ultradifferentiable functions and the boundary values of holomorphic functions
• Characterization of the separativity of ultradifferentiable classes
• On E. Borel's theorem
• Surjectivity of the restriction map to a compact in classes of ultradifferentiable functions
• Division by flat ultradifferentiable functions and sectorial extensions
• On generalized Lipschitz classes and Fourier series
• Injectivity and surjectivity of the asymptotic Borel map in Carleman ultraholomorphic classes
• Ultradifferentiable functions and Fourier analysis
• Whitney's extension theorem for ultradifferentiable functions of Beurling type
• Indices of O-regular variation for weight functions and weight sequences
• Flat functions in Carleman ultraholomorphic classes via proximate orders
• Summability in general Carleman ultraholomorphic classes
• A comparison of two different ways to define classes of ultradifferentiable functions
• Analytic continuation across a linear boundary
• Operators on Fock-type and weighted spaces of entire functions
• Composition in ultradifferentiable classes
• Linear Extension Operators for Ultradifferentiable Functions of Beurling Type on Compact Sets
• Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions
• LINEAR CONTINUOUS EXTENSION OPERATORS FOR GEVREY CLASSES ON POLYSECTORS
• Extension maps in ultradifferentiable and ultraholomorphic function spaces
• Extension of Whitney jets of controlled growth
• [https://portal.mardi4nfdi.de/wiki/Publication:4603546 Characterization of ultradifferentiable test functions defined by weight matrices in terms of their Fourier transform]
• Extension Gevrey et rigidité dans un secteur
• On the extension of Whitney ultrajets

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