We prove two kinds of Lyapunov type inequalities for pseudo-integrals. One discusses pseudo-integrals where pseudo-operations are given by a monotone and continuous function g. The other one focuses on the pseudo-integrals based on a semiring 0; 1 ½ Š; sup; ð Þ , where the pseudo-multiplication is generated. Some examples are given to illustrate the validity of these inequalities. As a generali...

In this article, we present a comprehensive discussion of new class inline microwave filters with transmission zeros in the response, namely, path filters. The main features are highlighted, and an original (synthesis-based) design approach is presented, relying on derivation suitable characteristic polynomials. addition to classical generalized Chebyshev characteristic, two characteristics int...

Abstract In the theory of orthogonal polynomials, as well in its intersection with harmonic analysis, it is an important problem to decide whether a given polynomial sequence $$(P_n(x))_{n\in \mathbb {N}_0}$$ ( P n x ) <...

We present a spectral method for solving elliptic equations which arise in general relativity, namely three-dimensional scalar Poisson equations, as well as generalized vectorial Poisson equations of the type ∆ ~ N + λ~ ∇(~ ∇ · ~ N) = ~ S with λ 6= −1. The source can extend in all the Euclidean space R, provided it decays at least as r−3 (scalar case) or r−4 (vectorial case). A multi-domain app...

We consider the differential equations y = λ0(x)y ′ + s0(x)y, where λ0(x), s0(x) are C −functions. We prove (i) if the differential equation, has a polynomial solution of degree n > 0, then δn = λnsn−1 − λn−1sn = 0, where λn = λ ′ n−1 + sn−1 + λ0λn−1 and sn = s ′ n−1 + s0λk−1, n = 1, 2, . . . . Conversely (ii) if λnλn−1 6= 0 and δn = 0, then the differential equation has a polynomial solution o...

The eponymous theorem of P.L. Wantzel [Wan] presents a necessary and sufficient criterion for angle trisectability in terms of the third Chebyshev polynomial T3, thus making it easy to prove that there exist non-trisectable angles. We generalize this theorem to the case of all Chebyshev polynomials Tm (Corollary 1.4.1). We also study the set m-Sect consisting of all cosines of m-sectable angles...

A generalized Chebyshev interpolation procedure increasing a fixed number of sample points at a time is developed and analyzed. It is incorporated into an efficient automatic quadrature scheme of Clenshaw-Curtis type. Numerical examples indicate that the present method is efficient not only for well-behaved functions but for those with discontinuous low order derivatives by virtue of adequate e...

This paper presents an efficient method for designing complex infinite impulse response digital filters in the complex Chebyshev sense. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez multiple exchange algorithm. Hence, the filter coefficients can be easily obtained by solving the eigenvalue problem to find the absolute minimum eigenvalue, ...