Chebyshev and Zolotarev perfect splines on an interval with zero boundary conditions (Q735847)

The Chebyshev and Zolotarev perfect splines are generalizations of the Chebyshev and Zolotarev polynomials, which were introduced at early stages of the development of approximation theory. This paper offers a further development of such scientific direction. The existence on an interval of Chebyshev and Zolotarev perfect splines with additional boundary properties is investigated. One theorem and seven lemmas are proved. Examples of application can be found in [\textit{D. A. Mikhalin}, Fundam. Prikl. Mat. 8, No. 4, 1047--1058 (2002; Zbl 1045.41004)].