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  • 1980-1984  (5)
  • 1
    Electronic Resource
    Electronic Resource
    On the abscissa of convergence for the Laplace transform of vector valued measures (1982)
    Springer
    Archiv der Mathematik 39 (1982), S. 455-462 
    Details
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01899547
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Stochastic operators, information, and entropy (1981)
    Springer
    Communications in mathematical physics 81 (1981), S. 31-38 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract For a stochastic operatorU on andL 1-space, i.eU is linear, positive, and norm preserving on the positive cone ofL 1, it is shown thatU decreases relative information between two nonnegativeL 1-functions. Furthermore it is shown that the following properties ofU are closely related:U is energy decreasing (energy preserving),U isH-decreasing, whereH is Boltzmann'sH-functional, and the Maxwell distributions are fixed points ofU.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01941799
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A perturbation theorem for the essential spectral radius of strongly continuous semigroups (1980)
    Springer
    Monatshefte für Mathematik 90 (1980), S. 153-161 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We generalize the Jörgens-Vidav semigroup perturbation theorem: If (U (t)), (V (t)) are s. c. semigroups, the generator of (V (t)) a bounded perturbation of the generator of (U (t)), and some remainder in the iteration series ofV (t) is strictly power compact, then the spectrum ofV (t) outside the spectral disc ofU (t) consists of eigenvalues of finite algebraic multiplicity. As a prerequisite, we show the invariance of components of the essential resolvent set of an operator under relatively power compact pertubations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01303264
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Calculation of the bidual for some function spaces (1980)
    Springer
    Mathematische Annalen 253 (1980), S. 63-87 
    Details
    ISSN: 1432-1807
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01457820
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    positivity in time dependent linear transport theory (1984)
    Springer
    Acta applicandae mathematicae 2 (1984), S. 311-331 
    Details
    ISSN: 1572-9036
    Keywords: 47D05 ; 82A70 ; 47B55 ; 47G05 ; 35K22 ; 35F15 ; 35C15 ; linear transport theory ; neutron transport equation ; Boltzmann equation ; semigroups ; perturbations ; irreducibility ; collision ; absorption ; scattering ; spectrum ; Dyson-Phillips expansion ; flows
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present methods using positive semigroups and perturbation theory in the application to the linear Boltzmann equation. Besides being a review, this paper also presents generalizations of known results and develops known methods in a more abstract setting. In Section 1 we present spectral properties of the semigroup operatorsW a(t) of the absorption semigroup and its generatorT a. In Section 2 we treat the full semigroup (W(t);t≧0) as a perturbation of the absorption semigroup. We discuss part of the problems (perturbation arguments and existence of eigenvalues) which have to be solved in order to obtain statements about the large time behaviour ofW(·). In Section 3 we discuss irreducibility ofW(·). In four appendices we present abstract methods used in Sections 1, 2 and 3.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02280857
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    Paper (German National Licenses)
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