A brief historical perspective of the Wiener–Hopf technique

Journal of Engineering Mathematics - Tập 59 Số 4 - Trang 351-358 - 2007
Jane B. Lawrie1, I. David Abrahams2
1Department of Mathematical Sciences, Brunel University, Uxbridge, UK
2School of Mathematics, University of Manchester, Manchester, UK

Tóm tắt

Từ khóa


Tài liệu tham khảo

http://www.en.wikipedia.org/wiki/Norbert_Wiener (Accessed on 24 September 2007)

Wiener N (1956). I am a Mathematician. Doubleday & Co., Inc.

Wiener N and Hopf E (1931). Über eine klasse singulärer integralgleichungen. Sem–Ber Preuss Akad Wiss 31: 696–706

Noble B (1988). Methods based on the Wiener–Hopf Technique, 2nd edn. Chelsea Publishing Company, New York

Carrier GF, Krook M and Pearson CE (2005). Functions of a complex variable. SIAM Publishing, Philadelphia

Muskhelishvili NI (1953). Singular integral equations, Translated from second edition Moscow (1946) by J.R.M. Radok. Noordhoff, Groningen

Hopf E (1934). Mathematical problems of radiative equilibrium. Cambridge Tract 31, Cambridge University Press, Cambridge

http://www.history.mcs.st-andrews.ac.uk/Biographies/Hopf_Eberhard.html (Accessed on 24 September 2007)

Sommerfeld A (1896). Mathematische theorie der diffraction. Math Ann 47: 317–374

Copson ET (1946). On an integral equation arising in the theory of diffraction. Quart J Math 17: 19–34

Carlson JF and Heins AE (1947). The reflection of an electromagnetic plane wave by an infinite set of plates, I. Quart Appl Math 4: 313–329

Carlson JF and Heins AE (1947). The reflection of an electromagnetic plane wave by an infinite set of plates, II. Quart Appl Math 5: 82–88

Levine H and Schwinger J (1948). On the radiation of sound from an unflanged circular pipe. Phys Rev 73: 383–406

Jones DS (1952). A simplifying technique in the solution of a class of diffraction problems. Quart J Math 3: 189–196

http://www.history.mcs.st-andrews.ac.uk/Biographies/Sneddon.html (Accessed on 24 September 2007)

Heins AE (1950) Systems of Wiener–Hopf equations. In: Proceedings of Symposia in Applied Mathematics II. McGraw-Hill, pp 76–81

Khrapkov AA (1971). Certain cases of the elastic equilibrium of an infinite wedge with a non-symmetric notch at the vertex, subjected to concentrated forces. Appl Math Mech (PMM) 35: 625–637

Khrapkov AA (1971). Closed form solutions of problems on the elastic equilibrium of an infinite wedge with nonsymmetric notch at the apex. Appl Math Mech (PMM) 35: 1009–1016

Daniele VG (1978). On the factorization of Wiener-Hopf matrices in problems solvable with Hurd’s method. IEEE Trans Antennas Propagat 26: 614–616

Rawlins AD (1975). The solution of a mixed boundary value problem in the theory of diffraction by a semi-infinite plane. Proc Roy Soc London A 346: 469–484

Rawlins AD (1985). A note on Wiener-Hopf matrix factorization. Quart J Mech Appl Math 38: 433–437

Idemen M (1979). A new method to obtain exact solutions of vector Wiener–Hopf equations. Zeit Angew Math Mech 59: 656–658

Hurd RA (1976). The Wiener–Hopf Hilbert method for diffraction problems. Canad J Phys 54: 775–780

Rawlins AD and Williams WE (1981). Matrix Wiener–Hopf factorization. Quart J Mech Appl Math 34: 1–8

Williams WE (1984). Recognition of some readily “Wiener–Hopf” factorizable matrices. IMA J Appl Math 32: 367–378

Jones DS (1984). Commutative Wiener–Hopf factorization of a matrix. Proc Roy Soc Lond A 393: 185–192

Jones DS (1984). Factorization of a Wiener–Hopf matrix. IMA J Appl Math 32: 211–220

Veitch BH and Abrahams ID (2007). On the commutative factorization of n  ×  n matrix Wiener–Hopf kernels with distinct eigenvalues. Proc Roy Soc London A 463: 613–639

Abrahams ID (1997). On the solution of Wiener-Hopf problems involving noncommutative matrix kernel decompositions. SIAM J Appl Math 57: 541–567

Koiter WT (1954). Approximate solution of Wiener–Hopf type integral equations with applications, parts I–III. Koninkl Ned Akad Wetenschap Proc B 57: 558–579

Carrier GF (1959). Useful approximations in Wiener–Hopf problems. J Appl Phys 30: 1769–1774

Kranzer HC and Radlow J (1962). Asymptotic factorization for perturbed Wiener–Hopf problems. J Math Anal Appl 4: 240–256

Kranzer HC and Radlow J (1965). An asymptotic method for solving perturbed Wiener–Hopf problems. J Math Mech 14: 41–59

Crighton DG (2001). Asymptotic factorization of Wiener–Hopf kernels. Wave Motion 33: 51–65

Abrahams ID and Wickham GR (1990). General Wiener–Hopf factorization of matrix kernels with exponential phase factors. SIAM J Appl Math 50: 819–838

Abrahams ID (2000). The application of Padé approximants to Wiener–Hopf factorization. IMA J Appl Math 65: 257–281

Abrahams ID (1996). Radiation and scattering of waves on an elastic half-space; a noncommutative matrix Wiener–Hopf problem. J Mech Phys Solids 44: 2125–2154

Abrahams ID (2002). On the application of the Wiener–Hopf technique to problems in dynamic elasticity. Wave Motion 36: 311–333

Jones DS (1952). Diffraction by a waveguide of finite length. Proc Camb Phil Soc 48: 118–134

Owen GW and Abrahams ID (2006). Elastic wave radiation from a high frequency finite-length transducer. J Sound Vib 298: 108–131

Lawrie JB and Guled IMM (2006). On tuning a reactive silencer by vaying the position of an internal membrane. J Acoust Soc Amer 120: 780–790

Maliuzhinets GD (1958). Excitation, reflection and emission of surface waves from a wedge with given face impedances. Soviet Phys Doklady 3: 752–755

Williams WE (1959). Diffraction of an E-polarized plane wave by an imperfectly conducting wedge. Proc R Soc Lond A 252: 376–393

Abrahams ID and Lawrie JB (1995). On the factorization of a class of Wiener–Hopf kernels. IMA J Appl Math 55: 35–47

Daniele VG (2003). The Wiener–Hopf technique for impenetrable wedges having arbitrary aperture angle. SIAM J Appl Math 63: 1442–1460

Daniele VG and Lombardi G (2006). Wiener–Hopf Solution for impenetrable wedges at skew incidence. IEEE Trans Antenn Prop 54: 2472–2485

Osipov AV and Norris AN (1999). The Malyuzhinets theory for scattering from wedge boundaries: a review. Wave Motion 29: 313–340

Budaev B (1995). Diffraction by wedges. Longman Scientific, London

Bernard JML (1998). Diffraction at skew incidence by an anisotropic impedance wedge in electromagnetism theory; a new class of canonical cases. J Phys A: Math Gen 31: 595–613

Osipov AV (2004) A hybrid technique for the analysis of scattering by impedance wedges. In: Proceedings of URSI Int Symp Electromagn Theory Pisa, Vol. 2, pp. 1140–1142

Lyalinov MA and Zhu NY (2003). Exact solution to diffraction problem by wedges with a class of anisotropic impedance faces: oblique incidence of a plane electromagnetic wave. IEEE Trans Antennas Propag 51: 1216–1220

Abrahams ID and Lawrie JB (1995). Travelling waves on a membrane: reflection and transmission at a corner of arbitrary angle, I. Proc R Soc London A 451: 657–683

Osipov AV (1996). Diffraction by a wedge with higher-order boundary conditions. Radio Sci 31: 1705–1720

Norris AN and Osipov AV (1997). Structural and acoustical wave interaction at a wedge-shaped junction of fluid-loaded plates. J Acoust Soc Amer 101: 867–876

Smyshlyaev VP (1993). The high-frequency diffraction of electromagnetic waves by cones of arbitrary cross sections. SIAM J Appl Math 53: 670–688

Babich VM, Dement’ev DB, Samokish BA and Smyshlyaev VP (2000). On evaluation of the diffraction coefficients for arbitrary ‘nonsingular’ directions of a smooth convex cone. SIAM J Appl Math 60: 536–573

Jones DS (1997). Scattering by a cone. Q Jl Mech Appl Math 50: 499–523

Bernard JML and Lyalinov MA (2001). Spectral domain solution and asymptotics for the diffraction by an impedance cone. IEEE Trans Antennas Propagat 49: 1633–1637

Antipov YA (2002). Diffraction of a plane wave by a circular cone with an impedance boundary condition. SIAM J Appl Math 62: 1122–1152

Kuiken HK (1985). Edge effects in crystal growth under intermediate diffusive-kinetic control. IMA J Appl Math 35: 117–129

Boersma J (1978). Note on an integral equation of viscous flow theory. J Eng Math 12: 237–243

Boersma J, Indenkleef JJE and Kuiken HK (1984). A diffusion problem in semconductor technology. J Eng Math 18: 315–333

Mysak LA and LeBlond PH (1972). The scattering of Rossby waves by a semi-infinite barrier. J Phys Oceanogr 2: 108–114

Levinson N (1966). Norbert Wiener. Bull Amer Math Soc 72: 1–32