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  • 1
    Electronic Resource
    Electronic Resource
    Integral Kernel Operators on Fock Space – Generalizations and Applications to Quantum Dynamics (1997)
    Springer
    Acta applicandae mathematicae 47 (1997), S. 49-77 
    Details
    ISSN: 1572-9036
    Keywords: white noise distribution theory ; Fock space ; integral kernel operator ; quantum stochastic integral ; quantum Langevin equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A general theory of operators on Boson Fock space is discussed in terms of the white noise distribution theory on Gaussian space (white noise calculus). An integral kernel operator is generalized from two aspects: (i) The use of an operator-valued distribution as an integral kernel leads us to the Fubini type theorem which allows an iterated integration in an integral kernel operator. As an application a white noise approach to quantum stochastic integrals is discussed and a quantum Hitsuda–Skorokhod integral is introduced. (ii) The use of pointwise derivatives of annihilation and creation operators assures the partial integration in an integral kernel operator. In particular, the particle flux density becomes a distribution with values in continuous operators on white noise functions and yields a representation of a Lie algebra of vector fields by means of such operators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005777929658
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Some remarks on induced representations of infinite discrete groups (1989)
    Springer
    Mathematische Annalen 284 (1989), S. 91-102 
    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/BF01443507
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  • 3
    Electronic Resource
    Electronic Resource
    Integral expression of some indecomposable characters of the infinite symmetric group in terms of irreducible representations (1990)
    Springer
    Mathematische Annalen 287 (1990), S. 369-375 
    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/BF01446899
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Constructing one-parameter transformations on white noise functions in terms of equicontinuous generators (1997)
    Springer
    Monatshefte für Mathematik 124 (1997), S. 317-335 
    Details
    ISSN: 1436-5081
    Keywords: 46F25 ; 35R15 ; 47B38 ; 60H99 ; White noise ; infinite dimensional Laplacian ; Cauchy problem ; equicontinuous operators ; one-parameter transformations ; infinitesimal generator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let $$\mathfrak{X}$$ be a barreled locally convex space. A continuous operator Ξ on $$\mathfrak{X}$$ is called anequicontinuous generator if {Ξ n /n!;n=0,1,2,...} is an equicontinuous family of operators. For each equicontinuous generator a one-parameter group of operators is constructed by means of power series. There is a one-to-one correspondence between the equicontinuous generators and the locally equicontinuous holomorphic one-parameter groups of operators. If two equicontinuous generators Ξ1, Ξ2 satisfy [Ξ1,Ξ2]=αΞ2 for some α∈ℂ thenaΞ1+bΞ2 is also an equicontinuous generator for anya, b∈ℂ. These general results are applied to a study of operators on white noise functions. In particular, a linear combination of the number operator and the Gross Laplacian, which are natural infinite dimensional analogues of a finite dimensional Laplacian, is always an equicontinuous generator. This result contributes to the Cauchy problems in white noise (Gaussian) space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01319042
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  • 5
    Electronic Resource
    Electronic Resource
    Complex White Noise and Coherent State Representations (2000)
    Springer
    Acta applicandae mathematicae 63 (2000), S. 283-291 
    Details
    ISSN: 1572-9036
    Keywords: complex white noise ; white noise operator ; coherent state ; exponential vector ; inverse S-transform
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An infinite-dimensional extension of a coherent state representation is discussed within the framework of white noise calculus. The exponential vectors (unnormalized coherent states) and the complex Gaussian integral play a role in such representations of a white noise function and of a white noise operator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1010771919136
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  • 6
    Book
    Book
    Exploring the Human Brain, Mind and Information Technology / (2002)
    Sendai :Konno Printing,
    Details
    Title: Exploring the Human Brain, Mind and Information Technology /
    Contributer: Nakamura, Tadao , Obata, Nobuaki , Sendai International Symposium 〈14, 2002, Tohoku〉 , TÄoku-Daigaku 〈Sendai, Miyagi-ken〉 , Tohoku Intelligent Cosmos Academic Society , Sendai International Symposium 14 Tohoku 2002.10.25-26
    Publisher: Sendai :Konno Printing,
    Year of publication: 2002
    Pages: 220 S. : , Ill., graph. Darst.
    Type of Medium: Book
    Language: English
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