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  • 1
    Electronic Resource
    Electronic Resource
    On discrete and continuous norms in Paley-Wiener spaces and consequences for exponential frames (1999)
    Springer
    The journal of Fourier analysis and applications 5 (1999), S. 193-201 
    Details
    ISSN: 1531-5851
    Keywords: Primary 30D15 ; 42C15 ; Secondary 30D10 ; 42C30 ; Paley-Wiener space ; entire functions of exponential type ; exponential frames ; discrete norms ; sampling theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is well known that for certain sequences {tn}n∈ℤ the usual Lp norm ∥·∥p in the Paley-Wiener space PW τ p is equivalent to the discrete norm ‖f‖p,{tn}:=(∑ n=−∞ ∞ |f(tn)|p)1/p for 1 ≤ p = 〈 ∞ and ‖f‖∞,{tn}:=sup n∈ℤ|f(tn| for p=∞). We estimate ∥f∥p from above by C∥f∥p, n and give an explicit value for C depending only on p, τ, and characteristic parameters of the sequence {tn}n∈ℤ. This includes an explicit lower frame bound in a famous theorem of Duffin and Schaeffer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01261609
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  • 2
    Electronic Resource
    Electronic Resource
    Elektroreduktion organischer Verbindungen, 20[ Darstellung von Bicyclo[n.1.0]alkanen durch elektrochemische Reduktion von 1,3-Dibromcycloalkanen (1992)
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 125 (1992), S. 1415-1419 
    Details
    ISSN: 0009-2940
    Keywords: Electrochemical reduction ; Bicyclo[n.1.0]alkanes ; Cycloalkanes, 1,3-dibromo ; Hunsdiecker reaction ; 1,3-Cycloalkanedicarboxylic acids ; Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Preparation of Bicyclo[n.1.0]alkanes by Electrochemical Reduction of 1,3-DibromocycloalkanesGood yields of bicyclo[2.1.0]pentane (17) and bicyclo[3.1.0]-hexane (3) are obtained on electroreduction of the corresponding 1,3-dibromocycloalkanes. The results do not depend upon the stereochemistry of the starting material (14 vs. 15 or 11 vs. 12).
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cber.19921250619
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    Paper (German National Licenses)
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