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  • 1
    Electronic Resource
    Electronic Resource
    Spectral measures, I: General theory in a topological vector space (1982)
    Springer
    Periodica mathematica Hungarica 13 (1982), S. 205-227 
    Details
    ISSN: 1588-2829
    Keywords: Primary 47B40 ; Secondary 28B05, 46A15, 46H05 ; Topological vector space ; spectral measures ; discontinuous scalar operators
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Part I of this paper is devoted to the general theory of spectral measures in topological vector spaces. We extend the Hilbert space theory to this setting and generalize the notion of spectral measure in some useful ways to provide a framework for Part II, etc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01847918
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Spectral measures, II: Characterization of scalar operators (1982)
    Springer
    Periodica mathematica Hungarica 13 (1982), S. 273-287 
    Details
    ISSN: 1588-2829
    Keywords: Primary 47B40 ; Secondary 28B05, 46A15, 46H05 ; Topological vector space ; Riesz theorem ; spectral measures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We continue the development of part I. The Riesz representation theorem is proved without assuming local convexity. This theorem is applied to give sufficient conditions for an operator (continuous or otherwise) to be “spectral”. A uniqueness problem is pointed out and the function calculus is extended to the case of several variables. A Radon—Nikodym theorem is proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01849240
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Spectral measures, III: Densely defined spectral measures (1984)
    Springer
    Periodica mathematica Hungarica 15 (1984), S. 189-203 
    Details
    ISSN: 1588-2829
    Keywords: Primary 47B40 ; Secondary 20B05, 46A15, 46H05 ; Topological vector space ; densely defined measures ; differential operators ; nonlocally convex spaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we extend the theory of spectral measures developed in Parts I and II to the case where values are assumed in the set of discontinuous (in normed spaces „unbounded”) operators. Examples of operators in nonlocally convex spaces are given, which have densely defined measures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02454168
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    Paper (German National Licenses)
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