## Journal of Integral Equations and Applications

### Explicit Solution of a Dirichlet-Neumann Wedge Diffraction Problem with a Strip

#### Article information

Source
J. Integral Equations Applications, Volume 15, Number 4 (2003), 359-383.

Dates
First available in Project Euclid: 5 June 2007

https://projecteuclid.org/euclid.jiea/1181074982

Digital Object Identifier
doi:10.1216/jiea/1181074982

Mathematical Reviews number (MathSciNet)
MR2058809

Zentralblatt MATH identifier
1069.47073

#### Citation

Castro, L.P.; Speck, F.-O.; Teixeira, F.S. Explicit Solution of a Dirichlet-Neumann Wedge Diffraction Problem with a Strip. J. Integral Equations Applications 15 (2003), no. 4, 359--383. doi:10.1216/jiea/1181074982. https://projecteuclid.org/euclid.jiea/1181074982

#### References

• H. Bart and V.E. Tsekanovskii, Matricial coupling and equivalence after extension, in Operator theory and complex analysis (T. Ando, et al., eds.), Oper. Theory Adv. Appl. 59, Birkhäuser, Basel, 1992, pp. 143-160.
• A. Böttcher, Yu.I. Karlovich and I.M. Spitkovsky, Convolution operators and factorization of almost periodic matrix functions, Oper. Theory Adv. Appl., Birkhäuser, Basel, 2002.
• L.P. Castro and F.-O. Speck, Regularity properties and generalized inverses of delta-related operators, Z. Anal. Anwendungen 17 (1998), 577-598.
• --------, Relations between convolution type operators on intervals and on the half-line, Integral Equations Operator Theory 37 (2000), 169-207.
• --------, Well-posedness of diffraction problems involving $n$ coplanar strips, in Singular integral operators, factorization and applications (A. Böttcher, et al., eds.), Oper. Theory Adv. Appl. 142, Birkhäuser, Basel, 2003, pp. 79-90.
• D.S. Jones, Methods in electromagnetic wave propagation, Vol. 1: Theory and guided waves, Vol. 2: Radiating waves, Clarendon Press, Oxford, 1987.
• N.K. Karapetiants and S.G. Samko, Equations with involutive operators, Birkhäuser, Boston, 2001.
• --------, On Fredholm properties of a class of Hankel operators, Math. Nachr. 217 (2000), 75-103.
• Yu.I. Karlovich and I.M. Spitkovskiĭ, Factorization of almost periodic matrix-valued functions and the Noether theory for certain classes of equations of convolution type, Math. USSR Izvestiya 34 (1990), 281-316.
• S. Lang, Real and functional analysis, 3rd ed., Springer-Verlag, New York, 1993.
• A.B. Lebre, E. Meister and F.S. Teixeira, Some results on the invertibility of Wiener-Hopf-Hankel operators, Z. Anal. Anwendungen 11 (1992), 57-76.
• E. Meister, F. Penzel, F.-O. Speck and F.S. Teixeira, Some interior and exterior boundary value problems for the Helmholtz equation in a quadrant, Proc. Roy. Soc. Edinburgh Sect. A 123 (1993), 275-294.
• --------, Two canonical wedge problems for the Helmholtz equation, Math. Methods Appl. Sci. 17 (1994), 877-899.
• E. Meister and F.-O. Speck, A contribution to the quarter-plane problem in diffraction theory, J. Math. Anal. Appl. 130 (1988), 223-236.
• --------, Modern Wiener-Hopf methods in diffraction theory, in Ordinary and partial differential equations, Vol. II (B. Sleeman, et al. ed.), Pitman Res. Notes, Math. Ser. 216, (1989), 130-171.
• E. Meister, F.-O. Speck and F.S. Teixeira, Wiener-Hopf-Hankel operators for some wedge diffraction problems with mixed boundary conditions, J. Integral Equations Appl. 4 (1992), 229-255.
• B. Noble, Methods based on the Wiener-Hopf technique for the solution of partial differential equations, Pergamon Press, London, 1958; Chelsea Publ. Co., New York, 1988.
• D. Sarason, Toeplitz operators with semi-almost periodic symbols, Duke Math. J. 44 (1977), 357-364.
• A. Sommerfeld, Mathematische Theorie der Diffraction, Math. Ann. 47 (1896), 317-374.
• F.-O. Speck, Mixed boundary value problems of the type of Sommerfeld's half-plane problem, Proc. Roy. Soc. Edinburgh Sect. A 104 (1986), 261-277.
• E.M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, 1970.
• F.S. Teixeira, Diffraction by a rectangular wedge: Wiener-Hopf-Hankel formulation, Integral Equations Operator Theory 14 (1991), 436-454.
• H. Triebel, Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam, 1978.
• E. Yamashita, ed., Analysis methods for electromagnetic wave problems, Artech House, London, 1990.