On the spectra of a quaternion singular integral operator and its components on spatial surfaces
Keywords:
quaternion, differentiable function, hyperholomorphic function, singular integral Cauchy operator, spectrumAbstract
On the spectra of a quaternion singular integral operator and its components on spatial surfaces.
References
O. F. Gerus, V. N. Kutrunov, M. Shapiro, On the spectra of some integral operators related to the potential theory in the plane, Mathematical Methods in the Applied Sciences 33 (2010), 1685–1691.
O. F. Gerus, On spectrum of the reduced singular integral Cauchy operator and its components, Zb. Pr. Inst. Mat. NAN Ukr. 9, no. 2 (2012), 87–94 (Russian).
O. F. Gerus, M. V. Shapiro On a Cauchy-type integral related to the Helmholtz operator in the plane, Boletin de la Sociedad Matem´atica Mexicana 10, no. 1 (2004), 63–82.
B. V. Shabat, Introduction to complex analysis. Part 1. Functions of one variable, ”Nauka”, Moscow (1976) (Russian).
A. S. Meylekhzon, On monogenity of quaternions, Doklady Acad. Nauk SSSR 59 (1948), 431–434.
G.Moisil, N. Theodoresco, Functions holomorphes dans l’espace, Mathematica (Cluj) 5 (1931), 142–159.
S. A. Plaksa, V. S. Shpakivskyi, Cauchy theorem for a surface integral in commutative algebras, Complex Variables and Elliptic Equations 59 (2014), 110–119.
O. F. Herus, On the Cauchy theorem for hyperholomorphic functions of spatial variable, Journal of Mathematical Sciences 229 (2018), 1–6.
P. Mattila, Geometry of sets and measures in Euclidean spaces. Fractals and rectifiability, Cambridge University Press (1995).
V. V. Kravchenko, M. V. Shapiro Integral representations for spatial models of mathematical physics, Addison Wesley Longman, Pitman Research Notes in Mathematics Series 351 (1996).
R. A. Blaya, J. B. Reyes, M. Shapiro On the Laplasian vector fields theory in domains with rectifiable boundary, Mathematical Methods in the Applied Sciences 29 (2006), 1861–1881.
R. A. Blaya, J. B. Reyes, Boundary value problems for quaternionic monogenic functions on non-smooth surfaces, Adv. Appl. Clifford algebras 9 (1999), 1–22.
V. Hudson, J. Pym, Applications of functional analysis and operator theory, Math. In Science and Engineering, London: Academic Press 146 (1980).
