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Digitale Medien

Double-knife EDGE problems with elastic/plastic type screens (1991)

Meister, E. ; Rawlins, A. D. ; Speck, F. -O.

Springer

Integral equations and operator theory 14 (1991), S. 373-389

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ISSN: 1420-8989

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract A problem of diffraction of a wave by a pair of semi-infinite screens is considered. The screens are lined with two different wave bearing materials that can support surface waves. This type of problem arises in the propagation and, scattering of acoustic and electromagnetic waves by surface wave guides. To be specific, we shall couch our problem in terms of acoustics. These diffraction problems for two parallel wave bearing screens lead to boundary value problems which are governed by the Helmholtz equation, and some specific third kind boundary conditions. Such problems are shown to be well-posed for finite energy space solutions. Their representation is given by means of the canonical factorization of a non-rational matrix function.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01218503

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2

Digitale Medien

Relations between convolution type operators on intervals and on the half-line (2000)

Castro, L. P. ; Speck, F. O.

Springer

Integral equations and operator theory 37 (2000), S. 169-207

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ISSN: 1420-8989

Schlagwort(e): 47B35 ; 45E10 ; 47A20 ; 47A05 ; 46E35 ; 47A68 ; 78A45

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract This paper is devoted to the question to obtain (algebraic and topologic) equivalence (after extension) relations between convolution type operators on unions of intervals and convolution type operators on the half-line. These operators are supposed to act between Bessel potential spaces,H s,p , which are the appropriate spaces in several applications. The present approach is based upon special properties of convenient projectors, decompositions and extension operators and the construction of certain homeomorphisms between the kernels of the projectors. The main advantage of the method is that it provides explicit operator matrix identities between the mentioned operators where the relations are constructed only by bounded invertible operators. So they are stronger than the (algebraic) Kuijper-Spitkovsky relation and the Bastos-dos Santos-Duduchava relation with respect to the transfer of properties on the prize that the relations depend on the orders of the spaces and hold only for non-critical orders:S − 1/p ∉ ℤ. For instance, (generalized) inverses of the operators are explicitly represented in terms of operator matrix factorization. Some applications are presented.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01192422

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3

Digitale Medien

Two canonical wedge problems for the Helmholtz equation (1994)

Meister, E. ; Penzel, F. ; Speck, F.-O. ; [weitere]

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 17 (1994), S. 877-899

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ISSN: 0170-4214

Schlagwort(e): Mathematics and Statistics ; Applied Mathematics

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik

Notizen: Boundary-transmission problems for two-dimensional Helmholtz equations in a quadrant and its complement, respectively, are considered in a Sobolev space setting. The first problem of a quadrant with Dirichlet condition on one face and transmission condition on the other is solved in closed form for the case where all the quadrants are occupied by the same medium. Unique solvability can also be shown in the case of two different media up to exceptional cases of wave numbers, while the Fredholm property holds in general. In the second problem, transmission conditions are prescribed on both faces. Similar results are obtained in the one-medium case, but the two-media case turns out to be more complicated and the equivalent system of boundary pseudodifferential equations cannot be completely analysed by this reasoning.

Zusätzliches Material: 3 Ill.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/mma.1670171104

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4

Digitale Medien

Diffraction by an acoustically transmissive or an electromagnetically dielectric half-plane (1991)

Rawlins, A. D. ; Meister, E. ; Speck, F. -O.

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 14 (1991), S. 387-402

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ISSN: 0170-4214

Schlagwort(e): Mathematics and Statistics ; Applied Mathematics

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik

Notizen: This work gives a mathematical model for an acoustically penetrable or electromagnetically dielectric half-plane. An approximate boundary condition is used that depends on the thickness of, and the material constants for, the half-plane. A solution is obtained, by using the approximate boundary condition, for the problem of a line source field diffracted by a penetrable/dielectric half-plane. The asymmetry of the approximate boundary condition results in a matrix Wiener-Hopf problem, which is solved explicitly.

Zusätzliches Material: 1 Ill.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/mma.1670140603

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5

Digitale Medien

Sommerfeld Diffraction Problems with Oblique Derivatives (1997)

Santos, A. Moura ; Speck, F.-O.

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 20 (1997), S. 635-652

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ISSN: 0170-4214

Schlagwort(e): Engineering ; Numerical Methods and Modeling

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik

Notizen: A class of diffraction problems for the two-dimensional Helmholtz equation is studied where the boundary conditions on a canonical screen contain oblique derivatives. The problem in weak formulation is reduced to a system of pseudodifferential equations on a half-line. The Fredholm property is characterized in dependence of the parameters, index formulas are given, and, if necessary, a normalization of the problem is implemented. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.

Zusätzliches Material: 4 Ill.

Materialart: Digitale Medien

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6

Digitale Medien

Factorization of a class of matrices generated by Sommerfeld diffraction problems with oblique derivatives (1997)

Lebre, A. B. ; Moura Santos, A. ; Speck, F.-O.

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 20 (1997), S. 1185-1198

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ISSN: 0170-4214

Schlagwort(e): Engineering ; Numerical Methods and Modeling

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik

Notizen: An explicit factorization of the Fourier symbol matrix functions generated by Sommerfeld diffraction problems with oblique derivatives is obtained. For this purpose a new prefactorization procedure is developed which makes use of factorization through weighted L2 spaces. These results yield a representation of a generalized inverse of the corresponding matrix Wiener-Hopf operator and the asymptotic behaviour of the solution at the edge of the screen. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Materialart: Digitale Medien

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