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Polynomially-divided solutions of bipartite self-differential functional equations

Dimitrov, Youri

Abstract Details

2006, Doctor of Philosophy, Ohio State University, Mathematics.
A real valued function Fon the interval [ a,b] is self-differentialif [ a,b] can be subdivided into a finite number of subintervals, and on each subinterval the derivative of Fis equal to Fwith the graph transformed by an affine map. In the four bipartite self-differential equations studied here, the interval [ 0,1] is decomposed into [ 0,1/2] and [ 1/2,1], and the affine transformed images of Fare aF(2x),F(2-2x),aF(1-2x),aF(2x-1).The bipartite self-differential equations have a solution for every value of the parameter aand initial value f(0)=c. The boundary value f(1)=dis determined from the values of aand c. When ais an odd power of 2there exist infinitely many continuously differentiable solutions. The solution is unique for all other values of a.
Gerald Edgar (Advisor)

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Citations

  • Dimitrov, Y. (2006). Polynomially-divided solutions of bipartite self-differential functional equations [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1155149204

    APA Style (7th edition)

  • Dimitrov, Youri. Polynomially-divided solutions of bipartite self-differential functional equations. 2006. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1155149204.

    MLA Style (8th edition)

  • Dimitrov, Youri. "Polynomially-divided solutions of bipartite self-differential functional equations." Doctoral dissertation, Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=osu1155149204

    Chicago Manual of Style (17th edition)