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Kravchenko, Vladislav V.; Tremblay, Sébastien

Spatial pseudoanalytic functions arising from the factorization of linear second order elliptic operators. (English) Zbl 1242.30039

Math. Methods Appl. Sci. 34, No. 16, 1999-2010 (2011).
The authors investigate mainly the following two problems: (1) biquaternionic Vekua-type equations with the derivative and antiderivative in the sense of Bers, and (2) exact solutions of Schrödinger type equations, based on the paper [J. Phys. A, Math. Gen. 39, No. 40, 12407–12425 (2006; Zbl 1106.30028)] by the first author.
Reviewer: Chuangan Hu (Palo Alto)

Cited in 4 Documents

MSC:

30G20 Generalizations of Bers and Vekua type (pseudoanalytic, \(p\)-analytic, etc.)
30G35 Functions of hypercomplex variables and generalized variables

Keywords:

generalized analytic functions; biquaternions; pseudoanalytic functions; Vekua equation; antiderivative; Schrödinger equation

Citations:

Zbl 1106.30028
Cite Review PDF
Full Text: DOI arXiv

References:

[1] Bers L 1952
[2] Vekua, Generalized Analytic Functions. Moscow: Nauka (in Russian) (1959) · Zbl 0092.29703
[3] Kravchenko, Applied Pseudoanalytic Function Theory (2009) · Zbl 1182.30002 · doi:10.1007/978-3-0346-0004-0
[4] Castillo Perez, Solution of boundary and eigenvalue problems for second order elliptic operators in the plane using pseudoanalytic formal powers, Mathematical Methods Applied Sciences 34 (4) pp 455– (2011) · Zbl 1210.35054
[5] Berglez, On generalized derivatives and formal powers for pseudoanalytic functions, Matematiche 62 (2) pp 29– (2007) · Zbl 1164.30026
[6] Malonek, Clifford Algebras and Their Application in Mathematical Physics, Dietrich V et al. (eds) pp 247– (1998) · doi:10.1007/978-94-011-5036-1_20
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[9] Kravchenko, On a factorization of second order elliptic operators and applications, Journal of Physics A: Mathematical and General 39 (40) pp 12407– (2006) · Zbl 1106.30028 · doi:10.1088/0305-4470/39/40/009
[10] Kravchenko, On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory, Journal of Physics A: Mathematical and General 41 (6) pp 65205– (2008) · Zbl 1139.81027 · doi:10.1088/1751-8113/41/6/065205
[11] Bers, An outline of the theory of pseudoanalytic functions, Bulletin of the American Mathematical Society 62 pp 291– (1956) · Zbl 0072.07703 · doi:10.1090/S0002-9904-1956-10037-2
[12] Kravchenko, On a relation of pseudoanalytic function theory to the two-dimensional stationary Schrödinger equation and Taylor series in formal powers for its solutions, Journal of Physics A: Mathematical and General 38 (18) pp 3947– (2005) · Zbl 1067.81032 · doi:10.1088/0305-4470/38/18/006
[13] Kravchenko, Applied Quaternionic Analysis (2003)
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[16] Korn, Mathematical Handbook for Scientists and Engineers (1961)
[17] Elkins, Orthogonal harmonic functions in space, Proc. Amer. Math. Soc. 8 pp 500– (1957) · Zbl 0080.08102 · doi:10.1090/S0002-9939-1957-0086136-0
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