Hölder continuous homomorphisms between infinite-dimensional Lie groups are smooth

Authors: Helge Glöckner

Source: Journal of Functional Analysis. 228:419-444

Subject Terms: Calculus of functions on infinite-dimensional spaces, Differentiability, Infinite-dimensional Lie group, Group Theory (math.GR), 01 natural sciences, Continuous and differentiable maps in nonlinear functional analysis, 22E65 (Primary) 26E15, 26E20, 26E30, 46T20, 58C20 (Secondary), Power map, FOS: Mathematics, 0101 mathematics, Calculus of functions taking values in infinite-dimensional spaces, Hölder continuity, Taylor expansion, Infinite-dimensional Lie groups and their Lie algebras: general properties, Lipschitz continuity, Smoothness, Functional Analysis (math.FA), Mathematics - Functional Analysis, Analysis on \(p\)-adic Lie groups, Homomorphism, Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions, non-Archimedean functional analysis, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, Non-Archimedean analysis, Mathematics - Group Theory, infinite-dimensional Lie group, Analysis, differentiability

File Description: application/xml

Access URL: http://arxiv.org/abs/math/0403251
https://www.sciencedirect.com/science/article/pii/S0022123605002892
https://core.ac.uk/display/82696344

Conveniently Hölder Homomorphisms are Smooth in the Convenient Sense: Conveniently Hölder homomorphisms are smooth in the convenient sense

Authors: Helge Glöckner

Source: Annals of Global Analysis and Geometry. 27:227-255

Subject Terms: Calculus of functions on infinite-dimensional spaces, Calculus of functions taking values in infinite-dimensional spaces, Infinite-dimensional Lie groups and their Lie algebras: general properties, Group Theory (math.GR), 01 natural sciences, Hölder condition, Continuous and differentiable maps in nonlinear functional analysis, Lie group, 22E65 (Primary) 26E15, 26E20, 46T20, 58C20 (Secondary), Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, convenient differential calculus, FOS: Mathematics, 0101 mathematics, Mathematics - Group Theory

File Description: application/xml

Access URL: http://arxiv.org/pdf/math/0404344v1.pdf
http://arxiv.org/abs/math/0404344
https://link.springer.com/article/10.1007/s10455-005-0040-z

Differential calculus over general base fields and rings: Differential calculus over general base fields and rings.

Authors: Karl-Hermann Neeb, Wolfgang Bertram, Helge Glöckner

Source: Expositiones Mathematicae. 22:213-282

Subject Terms: non-archimedian analysis, Mathematics(all), Calculus of functions on infinite-dimensional spaces, Calculus of functions taking values in infinite-dimensional spaces, Infinite-dimensional Lie groups and their Lie algebras: general properties, infinite-dimensional Lie groups, topological fields, polynomial maps, rational manifolds, 01 natural sciences, non-archimedean analysis, differential calculus, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, Non-Archimedean analysis, 0101 mathematics, infinite-dimensional manifolds

File Description: application/xml

Access URL: https://zbmath.org/2222515
https://doi.org/10.1016/s0723-0869(04)80006-9
https://www.sciencedirect.com/science/article/abs/pii/S0723086904800069
http://tubiblio.ulb.tu-darmstadt.de/8352/
https://hal.archives-ouvertes.fr/hal-00141431
https://www.sciencedirect.com/science/article/pii/S0723086904800069

Duality in the space of regulated functions and the play operator

Authors: Martin Brokate, Pavel Krejčí

Source: Mathematische Zeitschrift. 245:667-688

Subject Terms: Spaces of vector- and operator-valued functions, Calculus of functions taking values in infinite-dimensional spaces, Functions of bounded variation, generalizations, Denjoy and Perron integrals, other special integrals, 0101 mathematics, regulated functions, functions with bounded variation, 01 natural sciences, Hysteresis for ordinary differential equations

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/s00209-003-0563-6
https://documat.unirioja.es/servlet/articulo?codigo=2806754
https://dialnet.unirioja.es/servlet/articulo?codigo=2806668

A characterization of quasiconvex vector-valued functions

Authors: Benoist, Joël, Borwein, Jonathan M., Popovici, Nicolae

Contributors: Faculty of Science & Information Technology, School of Mathematical and Physical Sciences

Source: Proceedings of the American Mathematical Society. 131:1109-1113

Subject Terms: scalarization, Banach space, Calculus of functions taking values in infinite-dimensional spaces, 0211 other engineering and technologies, 02 engineering and technology, 01 natural sciences, vector-valued functions, quasiconvexity, polar cones, 0101 mathematics, quasiconvex vector-valued functions, Multi-objective and goal programming, Convexity of real functions of several variables, generalizations

File Description: application/xml

Access URL: https://www.ams.org/proc/2003-131-04/S0002-9939-02-06761-8/S0002-9939-02-06761-8.pdf
https://zbmath.org/1849931
https://doi.org/10.1090/s0002-9939-02-06761-8
http://docserver.carma.newcastle.edu.au/145/
https://dialnet.unirioja.es/servlet/articulo?codigo=321468
https://www.unilim.fr/pages_perso/joel.benoist/articles/bebopo.pdf
https://www.jstor.org/stable/1194189
https://www.ams.org/journals/proc/2003-131-04/S0002-9939-02-06761-8/home.html
https://www.ams.org/proc/2003-131-04/S0002-9939-02-06761-8/S0002-9939-02-06761-8.pdf

Flett′s mean value theorem in topological vector spaces: Flett's mean value theorem in topological vector spaces

Authors: Thomas Riedel, Prasanna K. Sahoo, Robert C. Powers

Source: International Journal of Mathematics and Mathematical Sciences, Vol 27, Iss 11, Pp 689-694 (2001)

Subject Terms: Calculus of functions taking values in infinite-dimensional spaces, Derivatives of functions in infinite-dimensional spaces, QA1-939, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, Gâteaux differentiable functions, 0101 mathematics, 01 natural sciences, Mathematics

File Description: application/xml

Access URL: http://downloads.hindawi.com/journals/ijmms/2001/894240.pdf
https://zbmath.org/1716633
https://doi.org/10.1155/s016117120101078x
https://doaj.org/article/e6f81bd06e094cf7a0913d039ac97858
https://www.hindawi.com/journals/ijmms/2001/894240/reprint/
https://downloads.hindawi.com/journals/ijmms/2001/894240.pdf
https://www.hindawi.com/journals/ijmms/2001/894240/
http://downloads.hindawi.com/journals/ijmms/2001/894240.pdf

On manifolds with non-negative Ricci curvature and Sobolev inequalities

Authors: Michel Ledoux

Source: Communications in Analysis and Geometry. 7:347-353

Subject Terms: Ricci curvature, Calculus of functions taking values in infinite-dimensional spaces, Riemann manifold, Sobolev inequality, compact support, 0101 mathematics, Integration on manifolds, measures on manifolds, 01 natural sciences, Global Riemannian geometry, including pinching

File Description: application/xml

Access URL: http://www.intlpress.com/site/pub/files/_fulltext/journals/cag/1999/0007/0002/CAG-1999-0007-0002-a007.pdf
https://www.intlpress.com/site/pub/files/_fulltext/journals/cag/1999/0007/0002/CAG-1999-0007-0002-a007.pdf
http://www.math.univ-toulouse.fr/~ledoux/Sobolev.pdf
https://intlpress.com/site/pub/pages/journals/items/cag/content/vols/0007/0002/a007/index.php

Functions of class $C^k$ without derivatives: Functions of class \(C^k\) without derivatives

Authors: Tuynman, G. M.

Source: Recercat. Dipósit de la Recerca de Catalunya
instname
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Publicacions Matemàtiques; Vol. 41, Núm. 2 (1997); p. 417-435

Subject Terms: topological abelian groups, Calculus of functions taking values in infinite-dimensional spaces, linearizing factor, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, functions of class \(C^k\), Fréchet and Gateaux differentiability in optimization

File Description: application/pdf; application/xml

Access URL: https://ddd.uab.cat/pub/pubmat/02141493v41n2/02141493v41n2p417.pdf
http://hdl.handle.net/2072/381566
https://ddd.uab.cat/record/13067
http://mat.uab.cat/pubmat/articles/view_doi/10.5565/PUBLMAT_41297_08
https://dialnet.unirioja.es/servlet/articulo?codigo=2137503
https://ddd.uab.cat/pub/pubmat/02141493v41n2/02141493v41n2p417.pdf
http://www.raco.cat/index.php/PublicacionsMatematiques/article/view/37904

Monotone and convex H*‐algebra valued functions: Monotone and convex \(H^*\)-algebra valued functions

Authors: Parfeny P. Saworotnow

Source: International Journal of Mathematics and Mathematical Sciences, Vol 19, Iss 3, Pp 473-479 (1996)

Subject Terms: convex function, convex functions, monotone functions, Calculus of functions taking values in infinite-dimensional spaces, Stieltjes integral, Banach *-algebra, saltus function, Integrals of Riemann, Stieltjes and Lebesgue type, 01 natural sciences, Monotonic functions, generalizations, Convexity of real functions in one variable, generalizations, Hilbert algebras, H*-algebra, trace-class, Hilbert Schmidt operators, QA1-939, \(H^*\)-algebra, Borel measure, Vector-valued measures and integration, 0101 mathematics, Mathematics

File Description: application/xml

Access URL: http://downloads.hindawi.com/journals/ijmms/1996/726464.pdf
https://doaj.org/article/b88a4145ecef4a7f871046fabd3239e6
https://www.hindawi.com/journals/ijmms/1996/726464/
https://downloads.hindawi.com/journals/ijmms/1996/726464.pdf

A chain rule for nonsmooth composite functions via minimisation

Authors: D. Ralph

Source: Bulletin of the Australian Mathematical Society. 49:129-137

Subject Terms: Programming in abstract spaces, composition of nonsmooth vector valued and real valued functions, Calculus of functions taking values in infinite-dimensional spaces, generalized gradient, Nonsmooth analysis, 0211 other engineering and technologies, chain rule, 02 engineering and technology, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/68E9C5FD09AC37C7B2E5BB5C930C15E1/S0004972700016178a.pdf/div-class-title-a-chain-rule-for-nonsmooth-composite-functions-via-minimisation-div.pdf
https://zbmath.org/563225
https://doi.org/10.1017/s0004972700016178
http://www.journals.cambridge.org/abstract_S0004972700016178

Locally compactly Lipschitzian mappings in infinite dimensional programming

Authors: B.M. Glover

Source: Bulletin of the Australian Mathematical Society. 47:395-406

Subject Terms: Programming in abstract spaces, Calculus of functions taking values in infinite-dimensional spaces, locally compactly Lipschitzian mapping, subgradient multifunction, Nonsmooth analysis, 0211 other engineering and technologies, 02 engineering and technology

File Description: application/xml

Access URL: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C8DE11545A91F04098484CEE19CE7055/S0004972700015227a.pdf/div-class-title-locally-compactly-lipschitzian-mappings-in-infinite-dimensional-programming-div.pdf
https://zbmath.org/427722
https://doi.org/10.1017/s0004972700015227
http://www.journals.cambridge.org/abstract_S0004972700015227
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0004972700015227

The Banach-Zarecki theorem for functions with values in metric spaces

Authors: Luděk Zajíček, Jakub Duda

Source: Proceedings of the American Mathematical Society. 133:3631-3633

Subject Terms: Lusin (N) condition, Calculus of functions taking values in infinite-dimensional spaces, Banach-Zarecki theorem, absolute continuity, Absolutely continuous real functions in one variable, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://www.ams.org/proc/2005-133-12/S0002-9939-05-07959-1/S0002-9939-05-07959-1.pdf
https://dialnet.unirioja.es/servlet/articulo?codigo=1377323
https://www.ams.org/journals/proc/2005-133-12/S0002-9939-05-07959-1/home.html

Some remarks about a notion of rearrangement

Authors: ALBERTI, GIOVANNI

Subject Terms: Calculus of functions taking values in infinite-dimensional spaces, Methods involving semicontinuity and convergence, relaxation, 0103 physical sciences, rearrangement, Inequalities involving derivatives and differential and integral operators, minimizers, 0101 mathematics, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, 01 natural sciences, non-local energy, increasing rearrangment, functional inequalities, Sobolev spaces, nonlocal models for phase separation, optimal profiles, nonlocal functionals

File Description: application/xml

Access URL: https://zbmath.org/1529126
https://hdl.handle.net/11568/160995
http://eudml.org/doc/84413

Seminorn generating relations and their Minkowski functionals: Seminorm generating relations and their Minkowski functionals

Authors: Száz, Árpád, Túri, József

Subject Terms: QA Mathematics / matematika, Calculus of functions taking values in infinite-dimensional spaces, Topological linear spaces and related structures, multivalued mapping, Minkowski functionals, seminorm generating relation, absorbing, balanced, convex sets

File Description: application/xml; text

Access URL: https://zbmath.org/1603938

A generalization of l'Hopital's rule via absolute continuity and Banach modules: A generalization of l'Hôpital's rule via absolute continuity and Banach modules

Authors: VIANELLO, MARCO

Subject Terms: absolutely continuous functions, Calculus of functions taking values in infinite-dimensional spaces, complex Banach algebra, Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems, l'Hôpital's rule, Absolutely continuous real functions in one variable, Banach module

File Description: application/xml

Access URL: https://zbmath.org/465119
https://hdl.handle.net/11577/123991

Contribution to the Theory of Generalized Derivatives: Contribution to the theory of generalized derivatives

Authors: Siegfried Gähler

Source: Zeitschrift für Analysis und ihre Anwendungen. 5:367-376

Subject Terms: Calculus of functions on infinite-dimensional spaces, Derivatives of functions in infinite-dimensional spaces, Calculus of functions taking values in infinite-dimensional spaces, Nonlinear programming, Methods involving semicontinuity and convergence, relaxation, product rule, Euler differential equation, mean value theorem, Fréchet and Gateaux differentiability in optimization, quotient rule, Ordered topological linear spaces, vector lattices, Lower and upper derivatives

File Description: application/xml

Access URL: http://www.ems-ph.org/doi/10.4171/ZAA/204

Sulla differenziabilità delle funzioni a valori in uno spazio reale di Banach riflessivo: Sulla differenziabilita delle funzioni a valori in uno spazio reale di Banach riflessivo

Authors: Cristina Di Bari

Source: Rendiconti del Circolo Matematico di Palermo. 28:229-238

Subject Terms: Calculus of functions taking values in infinite-dimensional spaces, differentiability of functions in several variables with values in reflexive Banach spaces, Continuity and differentiation questions, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/content/pdf/10.1007/BF02844097.pdf
https://link.springer.com/article/10.1007%2FBF02844097

Weak compactness of Fréchet-derivatives: application to composition operators: Weak compactness of Fréchet-derivatives. Application to composition operators

Authors: Peter Dierolf, Jürgen Voigt

Source: Journal of the Australian Mathematical Society. 29:399-406

Subject Terms: Representation and superposition of functions, weakly compact map, Banach spaces, Fréchet derivatives, Calculus of functions taking values in infinite-dimensional spaces, compactness properties, Linear operators on function spaces (general), Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, calculus of variations, superposition operators, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/3635149
https://www.cambridge.org/core/journals/journal-of-the-australian-mathematical-society/article/weak-compactness-of-frechetderivatives-application-to-composition-operators/843F1283A2D9B3B61FF044668BA7AE5C
http://www.journals.cambridge.org/abstract_S1446788700021558

V-subdifferentials of convex operators

Authors: Lionel Thibault

Source: Journal of Mathematical Analysis and Applications. 115:442-460

Subject Terms: Calculus of functions on infinite-dimensional spaces, Derivatives of functions in infinite-dimensional spaces, Calculus of functions taking values in infinite-dimensional spaces, Methods involving semicontinuity and convergence, relaxation, Applied Mathematics, Convex sets in topological linear spaces, Choquet theory, 0211 other engineering and technologies, 02 engineering and technology, Fréchet and Gateaux differentiability in optimization, 01 natural sciences, Nonlinear programming, V-subdifferential, convex operator, 0101 mathematics, Convex sets in topological vector spaces (aspects of convex geometry), Analysis

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/0022247X86900077#!
https://www.sciencedirect.com/science/article/abs/pii/0022247X86900077

Die richtigen R�ume f�r Analysis im Unendlich-Dimensionalen: Die richtigen Räume für Analysis im Unendlich-Dimensionalen

Authors: Kriegl, A.

Source: Monatshefte f�r Mathematik. 94:109-124

Subject Terms: Derivatives of functions in infinite-dimensional spaces, Calculus of functions taking values in infinite-dimensional spaces, c-infinity-complete bornological spaces, Spaces defined by inductive or projective limits (LB, LF, etc.), differentiable curves in locally convex spaces, 01 natural sciences, Article, 12. Responsible consumption, 510.mathematics, Barrelled spaces, bornological spaces, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), LF-spaces, 8. Economic growth, 11. Sustainability, 0103 physical sciences, Closed categories (closed monoidal and Cartesian closed categories, etc.), symmetrically monoidal closed, 0101 mathematics, 10. No inequality, Open mapping and closed graph theorems, completeness (including \(B\)-, \(B_r\)-completeness)

File Description: application/xml; image/jpeg; application/pdf

Access URL: https://zbmath.org/3770348
https://doi.org/10.1007/bf01301929
https://link.springer.com/article/10.1007/BF01301929