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Author: Yuksel, UgurPublisher: Springer Basel Ag

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Now showing 1 - 3 of 3
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    On a Dirichlet Problem for a Generalized Beltrami Equation
    (Springer Basel Ag, 2018) Gurlebeck, Klaus; Yuksel, Ugur
    In this article we study a Dirichlet problem for a hypercomplex Beltrami equation. We prove the existence of a unique solution of the problem and give a representation formula for the solution.
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    Citation - WoS: 4
    Citation - Scopus: 7
    Necessary and Sufficient Conditions for First Order Differential Operators To Be Associated With a Disturbed Dirac Operator in Quaternionic Analysis
    (Springer Basel Ag, 2015) Abbas, Usman Yakubu; Yuksel, Ugur
    Recently the initial value problem partial derivative(t)u = Lu :- Sigma(3)(i=1) A((i)) (t, x)partial derivative(xi) u + B(t, x)u + C(t, x) u(0, x) = u(0)(x) has been solved uniquely by N. Q. Hung (Adv. appl. Clifford alg., Vol. 22, Issue 4 (2012), pp. 1061-1068) using the method of associated spaces constructed by W. Tutschke (Teubner Leipzig and Springer Verlag, 1989) in the space of generalized regular functions in the sense of quaternionic analysis satisfying the equation D(alpha)u = 0, where D(alpha)u := Du + alpha u, alpha is an element of R, and D = Sigma(3)(j=1) e(j)partial derivative(xj) is the Dirac operator, x = (x(1), x(2), x(3)) is the space like variable running in a bounded domain in R-3 , and t is the time. The author has proven only sufficient conditions on the coefficients of the operator L under which L is associated with the operator D-alpha, i.e. L transforms the set of all solutions of the differential equation D(alpha)u = 0 into solutions of the same equation for fixedly chosen t. In the present paper we prove necessary and sufficient conditions for the underlined operators to be associated. This criterion makes it possible to construct all linear operators L for which the initial value problem with an arbitrary initial generalized regular function is always solvable.
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    Citation - WoS: 3
    Citation - Scopus: 5
    Necessary and Sufficient Conditions for Associated Differential Operators in Quaternionic Analysis and Applications To Initial Value Problems
    (Springer Basel Ag, 2013) Yuksel, Ugur
    This paper deals with the initial value problem of type in the space of generalized regular functions in the sense of Quaternionic Analysis satisfying the differential equation where is the time variable, x runs in a bounded and simply connected domain in is a real number, and is the Cauchy-Fueter operator. We prove necessary and sufficient conditions on the coefficients of the operator under which is associated with the operator , i.e. transforms the set of all solutions of the differential equation into solutions of the same equation for fixedly chosen t. This criterion makes it possible to construct operators for which the initial value problem is uniquely soluble for an arbitrary initial generalized regular function u (0) by the method of associated spaces constructed by W. Tutschke (Teubner Leipzig and Springer Verlag, 1989) and the solution is also generalized regular for each t.