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  • 1
    Electronic Resource
    Electronic Resource
    Theorems of Stone-Weierstrass type for non-compact spaces (1968)
    Springer
    Mathematische Zeitschrift 104 (1968), S. 226-230 
    Details
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01110290
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Infinite dimensional calculus allowing nonconvex domains with empty interior (1990)
    Springer
    Monatshefte für Mathematik 110 (1990), S. 145-166 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We develop differentiation theory based on a new definition of derivative: in terms of integrals of curves. It applies to a very wide class of domains. Some ‘elementary’ maps between Fréchet spaces, excluded from calculus by previous theories, now emerge as smooth maps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01302783
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Infinite dimensional holomorphy via categorical differential calculus (1991)
    Springer
    Monatshefte für Mathematik 111 (1991), S. 55-68 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We establish that the category of hological spaces is equipped for calculus with complex scalars. This provides a theory of infinite dimensional holomorphy which allows maps to have nonconvex domains with empty interior. Some relatively elementary functions, hitherto excluded by the restrictive definitions of other theories, emerge as holomorphic maps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01299277
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Differential calculus founded on an isomorphism (1993)
    Springer
    Applied categorical structures 1 (1993), S. 51-57 
    Details
    ISSN: 1572-9095
    Keywords: Primary: 58C20 ; Secondary 46M15 ; 46G05 ; Categorical methods ; differential calculus ; differentiation theory ; foundational isomorphism
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper founds calculus on a natural isometric linear isomorphism. Once this Foundational Isomorphism is proved (with elementary Banach space methods) several familiar calculus properties of continuous curves drop out as quick corollaries. Then the calculus can be further developed in very general setting via categorical methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00872985
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Holomorphy in convergence spaces (1993)
    Springer
    Applied categorical structures 1 (1993), S. 233-245 
    Details
    ISSN: 1572-9095
    Keywords: Primary: 46G20 ; Secondary: 58B12, 46M40 ; Infinite dimensional holomorphy ; closed-embedded linear convergence spaces ; analyte ; categorical methods ; categorical differentiation theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We introduce a new approach to infinite dimensional holomorphy. Cast in the setting of closed-embedded linear convergence spaces and based on a categorical definition of derivative, our theory applies beyond the traditional open domains. It reaches certain domains with empty interior (that arise naturally in Fréchet spaces) and gives a fully fledged differential calculus. On open domains our approach provides a new characterization of holomorphic maps. Thus earlier theories become expanded as well as strengthened.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00880045
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  • 6
    Electronic Resource
    Electronic Resource
    Newton’s Method and Frobenius–Dieudonné Theorem in Nonnormable Spaces (1997)
    Springer
    Applied categorical structures 5 (1997), S. 205-216 
    Details
    ISSN: 1572-9095
    Keywords: Newton’s method ; nonnormable spaces ; nonlinear operators ; nonlinear equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We establish, via auxiliary categories, a version of Newton’s method applicable to nonnormable spaces. We illustrate it with an application to perturbation of functional equations on unbounded domains. Under suitable conditions, the known solution of the unperturbed equation initiates a sequence of Newton iterates that converges to the solution of the perturbed equation. The conditions posed are those required to make Newton’s method work. We also generalize the Frobenius–Dieudonné existence-uniqueness theorem for initial value problems for a vector variable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008690318367
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  • 7
    Electronic Resource
    Electronic Resource
    Foundational Isomorphisms in Continuous Differentiation Theory (1998)
    Springer
    Applied categorical structures 6 (1998), S. 127-135 
    Details
    ISSN: 1572-9095
    Keywords: categorical methods ; differential calculus ; differentiation theory ; foundational isomorphism ; linear convergence spaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We provide an elementary proof of existence for the Foundational Isomorphism in each of the categories of convergence spaces, compactly generated topological spaces and sequential convergence spaces. This isomorphism embodies the ‘germ’ of differentiation and its inverse the ‘germ’ of integration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008631405316
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    Paper (German National Licenses)
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