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Application of the cosine function
The Mathematics Teacher, 1963A project for the trigonometry ...
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A Cosine Functional Equation with Restricted Argument
Canadian Mathematical Bulletin, 1974We name a functional equation with restricted argument one in which at least one of the variables is restricted to a certain discrete subset of the domain of the other variable(s). In particular, the subset may consist of a single element.The purpose of this paper is to present a functional equation satisfied only by cosine functions.
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On an exponential-cosine functional equation
Periodica Mathematica Hungarica, 1988Let X be a Banach space, \({\mathbb{C}}\) the complex numbers, and let f: \(X\to {\mathbb{C}}\) satisfy the functional equation \((A)\quad f(x+y)+(2f^ 2(y)- f(2y))f(x-y)=2f(x)f(y).\) (A) generalizes the well-studied equations of D'Alembert and Cauchy: \((D)\quad F(x+y)+F(x-y)=2F(x)F(y),\) and \((C)\quad G(x+y)=G(x)G(y),\) respectively.
Parnami, J. C. +2 more
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On the Cosine Functional Equation
1968Application of functional equations has preceded the development of a systematic theory of functional equations. One of the important applications of functional equations is a functional characterization of various functions like Euler’s Γ function, Lebesgue’s singular function, cyclic functions, polynomials, exponential and logarithmic functions, etc.
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A Cosine Functional Equation in Hilbert Space
Canadian Journal of Mathematics, 1960Throughout this paper R denotes the set of all real numbers, m(K) the Lebesgue measure of K ⊆ R, H a Hilbert space, L(H) the set of all linear continuous mappings of H into H, endowed with the usual structure of a Banach space.We consider the mapping F of the set R into L(H) such thatholds for all x, y ∈ R. In (2) we have solved this equation under the
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Chaos for Cosine Operator Functions Generated by Shifts
International Journal of Bifurcation and Chaos, 2014Let 1 ≤ p < ∞. We give the sufficient and necessary condition for cosine operator functions, generated by bilateral weighted shifts on ℓp(ℤ), to be chaotic. Moreover, such a cosine operator function is chaotic if, and only if, its weighted shift is chaotic.
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Discrete Approximations of Cosine Operator Functions. I
SIAM Journal on Numerical Analysis, 1982Summary: We are concerned with the approximation of cosine operator functions which appear in a natural way in the study of the Cauchy problem for second order evolution equations. We derive both qualitative and quantitative convergence theorems characterizing the convergence of cosine operator functions in terms of their infinitesimal generators, and ...
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Fourier-Cosine Method for Finite-Time Gerber--Shiu Functions
SIAM Journal of Scientific Computing, 2021Sheung Chi Phillip Yam, Hailiang Yang
exaly