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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    The journal of Fourier analysis and applications 5 (1999), S. 193-201 
    ISSN: 1531-5851
    Schlagwort(e): Primary 30D15 ; 42C15 ; Secondary 30D10 ; 42C30 ; Paley-Wiener space ; entire functions of exponential type ; exponential frames ; discrete norms ; sampling theorem
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 123 (1990), S. 1733-1737 
    ISSN: 0009-2940
    Schlagwort(e): Dithiolactones ; Electroreduction ; Haloalkanedithioates ; Thioacetals, semicyclic ; Chemistry ; Inorganic Chemistry
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: Intramolecular cyclization occurs on electroreduction of the methyl -haloalkanedithioates 1 in methanol. The expected semicyclic thioacetals 2 are formed according to an ECEH mechanism. The biheterocycles 12 result from dimerization of intermediate radicals whereas the semicyclic ketene dithio-acetals 13 are formed by non-electrochemical processes. The 2-(methylthio)thiolanes 2 a and 16 are obtained with much higher yields and better selectivity by co-electroreduction of the -dithio-lactones 15 in the presence of dimethyl sulfate.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 3
    Digitale Medien
    Digitale Medien
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 125 (1992), S. 127-141 
    ISSN: 0009-2940
    Schlagwort(e): Dithiopivaloates, S-aryl, S-benzyl ; Electroreduction ; Chemistry ; Inorganic Chemistry
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: Electroreduction of Organic Compounds, 19.  -  Formation of Benzoanellated Sulfur Heterocycles by Intramolecular Cathodic Cyclization of Dithiocarboxylic EstersCathodic reduction of aryl (3) and benzyl (5) dithiopivaloates and related dithioesters with leaving groups at the benzene ring or a side chain yield the sulfur heterocycles 23, 30 - 32, and 34 depending on the nature of the starting material and the reaction conditions. In case of the α-oxo-dithioester 22, thioindigo (44) is formed.  -  The corresponding thioamides 14, 16, and 18 show a strong tendency to reductive dehalogenation but the S,N-heterocycles 38 and 39 are also formed in minor amounts.  -  The formation of the rearranged products 29 - 32, and 34 is discussed in terms of C,S-splitting in the primarily formed radical anion and subsequent C,C-coupling of the fragments and follow-up reactions.
    Zusätzliches Material: 7 Tab.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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