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  • 1
    Digitale Medien
    Digitale Medien
    Multiresolution properties of the wavelet Galerkin operator (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1440-1443 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: This paper extends recent results by the author [J. Math. Phys. 31, 1898 (1990), J. Math. Phys. 32, 57 (1991)] that show a scaling parameter sequence h yields an orthonormal wavelet basis for L2(R) if and only if an associated operator Sh has eigenvalue 1 with multiplicity 1. The operator transforms a sequence a by Sh(a)(k)=2Σm,n∼(h(m))h(n)a(2k+m−n). A correspondence is derived between Sh and Galerkin projection operators related to the multiresolution analysis defined by the orthonormal wavelet basis. The spectrum of Sh is characterized in terms of the Fourier modulus of the (unique) scaling function φ that satisfies φ(x)=2Σnh(n)φ(2x−n). This characterization yields several results including a direct, alternate proof that the eigenvalue 1 of Sh has multiplicity 1.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.529300
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  • 2
    Digitale Medien
    Digitale Medien
    Necessary and sufficient conditions for constructing orthonormal wavelet bases (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 57-61 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: This paper proves a previous conjecture of the author characterizing sequences h∈l2(Z) that yield orthonormal wavelet bases of L2(R) in terms of the multiplicity of the eigenvalue 1 of an operator associated to h. The proof utilizes a result of Cohen characterizing these sequences in terms of the real zeros of their Fourier transforms. The mapping from sequences to wavelets is shown to define a continuous mapping from a subset of l2(Z) into L2(R). Related conjectures are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.529093
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  • 3
    Digitale Medien
    Digitale Medien
    Tight frames of compactly supported affine wavelets (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1898-1901 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: This paper extends the class of orthonormal bases of compactly supported wavelets recently constructed by Daubechies [Commun. Pure Appl. Math. 41, 909 (1988)]. For each integer N≥1, a family of wavelet functions ψ having support [0,2N−1] is constructed such that {ψjk(x)=2j/2ψ(2jx−k) kj,k∈Z} is a tight frame of L2(R), i.e., for every f∈L2(R), f=c∑jk 〈ψjk||f〉ψjk for some c〉0. This family is parametrized by an algebraic subset VN of R4N. Furthermore, for N≥2, a proper algebraic subset WN of VN is specified such that all points in VN outside of WN yield orthonormal bases. The relationship between these tight frames and the theory of group representations and coherent states is discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.528688
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  • 4
    Digitale Medien
    Digitale Medien
    High-power Nd:glass laser transmission through optical fibers and its use in acceleration of thin foil targets (1990)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 67 (1990), S. 3297-3301 
    Details
    ISSN: 1089-7550
    Quelle: AIP Digital Archive
    Thema: Physik
    Notizen: Measurements on commercially available fused silica fibers and fiber tapers have shown that Nd:glass laser pulses of irradiance 〉3.5 GW cm−2 can be transmitted without bulk or surface damage. Optical energy at the fiber output can be used for efficient acceleration of thin metal foils. For 0.025-mm-thick aluminum coupled to a 0.2-mm-diam fiber, target foil velocities up to 2.3 km s−1 have been achieved with very modest laser energies (〈25 mJ).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.345364
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  • 5
    Digitale Medien
    Digitale Medien
    Optically generated liquid crystal gratings (1994)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 65 (1994), S. 2542-2544 
    Details
    ISSN: 1077-3118
    Quelle: AIP Digital Archive
    Thema: Physik
    Notizen: Optically controlled planar orientation of liquid crystal molecules with polarized light is used to make phase gratings in liquid crystal media. The electro-optical properties of liquid crystal linear and chirped gratings are discussed. © 1994 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.112629
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