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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
    ESR-Untersuchungen an Carbonsäureestern, 12. Bildung von 9-Fluorenon-Radikalanionen durch Elektrolyse von sterisch gehinderten Biphenyl-2-dithiocarbonsäure-methylestern (1989)
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 122 (1989), S. 1009-1012 
    Details
    ISSN: 0009-2940
    Keywords: ESR, biphenyl-2-carbodithioates ; 9-Fluorenones, sterical hindrance ; Radical anions ; Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Formation of 9-Fluorenone Radical Anions during Electroreduction of Sterically Hindered Methyl Biphenyl-2-dithiocarboxylatesESR signals due to the radical anions of the 9-fluorenones 4 and 5 are observed besides the spectra of the radical anions of the tert-butylated methyl biphenyl-2-dithiocarboxylates 1 and 2 if the latter are electroreduced in dimethylformamide or acetonitrile. A mechanism for the observed reaction is suggested.
    Notes: Nach Elektroreduktion der tert-butylierten Biphenyl-2-dithiocarbonsäure-methylester 1 und 2 in Dimethylformamid oder Acetonitril beobachteten wir neben den ESR-Spektren der entsprechenden Radikalanionen die Signale von Radikalanionen der 9-Fluorenone 4 und 5. Ein Mechanismus für die Bildung der 9-Fluorenon-Ketyle wird vorgeschlagen.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cber.19891220534
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    Paper (German National Licenses)
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