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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of theoretical probability 6 (1993), S. 187-193 
    ISSN: 1572-9230
    Keywords: Fourier transform ; characteristic function ; spherical partial sum ; Gibbs' phenomenon
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A density functionf(x),x∈R n is said to bepiecewise smooth if for eachx∈R n , the mean value function $$r \to M_r f(x): = \smallint _{S^{n - 1} } f(x + r\omega )$$ is piecewiseC ∞ with compact support. (dω is normalized surface measure on the unit sphere). The Fourier transform is $$\hat f(\mu ) = \smallint _{R^n } f(x)e^{i〈 \mu ,x 〉 } dx$$ with spherical partial sum $$f_R (x) = (2\pi )^{ - n} \smallint _{|\mu | \leqslant R} \hat f(\mu )e^{ - i〈 \mu ,x 〉 } d\mu $$ . Theorem. For suchf, lim r↑∞ f R (x)=M 0+f(x) if and only ifr→M r f(x) hask=[(n−3)/2] continuous derivatives. ([]=integer part). Otherwise we have lim $$\inf _{R \uparrow \infty } R^{ - v} [f_R (x) - M_{0^ + } f(x)]〈 0〈 \lim \sup _{R \uparrow \infty } R^{ - v} [f_R (x) - M_{0^ + } f(x)]$$ where ν≥0 is uniquely determined.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Annals of global analysis and geometry 18 (2000), S. 347-369 
    ISSN: 1572-9060
    Keywords: eigenfunction ; Jacobi polynomials ; Laplacian ; symmetric spaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We find sharp conditions for the pointwise convergence ofeigenfunction expansions associated with the Laplace operator and otherrotationally invariant differential operators. Specifically, we considerthis problem for expansions associated with certain radially symmetricoperators and general boundary conditions and the problem in the contextof Jacobi polynomial expansions. The latter has immediate application toFourier series on rank one symmetric spaces of compact type.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 13 (1975), S. 189-196 
    ISSN: 1572-9613
    Keywords: Linearized Boltzmann equation ; jump Markov process ; path integral representation ; multiplicative functional
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract For the linearized Boltzmann equation with finite cross section, the solution is represented as an integral over the paths of a Markov jump process. The integral is only shown to converge conditionally, where the limiting process is defined by an increasing sequence of stopping times. The notion of local martingale plays an important role. A number of related kinetic models are also mentioned.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Applied mathematics & optimization 7 (1981), S. 137-139 
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We find upper and lower bounds for the first eigenvalue of the Laplacian on the two-sphere from which a disk has been removed, with Dirichlet conditions imposed on the resulting boundary. When the radius of the disk tends to zero our lower bound is sharper than that obtained by Del Grosso, Gerardi, and Marchetti in the preceding paper.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1572-9605
    Keywords: Josephson lattice ; resonance properties ; exact solution approach
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract Electromagnetic and superconducting properties are considered in superconducting films separated by thin oxide interlayers (the so-called superconductive lattices with microstructure). Using the planar X-Y model for superconductive lattices and taking account of dissipative effects of superconductive layers, we obtain a decomposition of current singularities in the dc current-voltage characteristics. Analytical functions are obtained, and an analysis is made of the hyperfine decomposition structure of current peaks in accordance with the numbern of layers and also in accordance with the determinedω 0,ω 1,ω 2, the eigenmodes which are determined by two-dimensional Josephson resonators. A complex spectrum of current peaks in the dc current-voltage characteristics is shown in our analysis. The growth of the numberm 1 of satellites from the principal peak with increase of the numbern of layers is observed. For some large numbern=n * of layers there is a tendency to an asymptotic saturation of the total number of satellites. In particular, the phenomenon of single peaks is observed for some intermediate numbern=n k of layers. In this case we have an intermediate layer, which shows the character of a one-dimensional long Josephson line. In the general case we can change parameters (n,ω 0,ω 1ω2) to get various properties in the dc current-voltage characteristics. Hysteresis is obtained for some values of the parameters. The characteristics defined through the exact solutions of the “non-Josephson” generation of the fluxon lattice,I n =I n (〈V〉), are presented.
    Type of Medium: Electronic Resource
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  • 6
    Title: Introduction to ordinary differential equations with Mathematica : an integrated multimedia approach + CD-ROM
    Author: Gray, Alfred
    Contributer: Mezzino, Michael , Pinsky, Mark A.
    Publisher: New York u. a.; Telos, Santa C :Springer,
    Year of publication: 1997
    Pages: 890 S.
    Type of Medium: Book
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