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Interpolation of cosine operator functions [PDF]

Annali di Matematica Pura ed Applicata, 1984
Given a strongly continuous cosine operator function C on \(R^+\) with values in the Banach algebra B(A) of bounded linear operators in a Banach space A and infinitesimal generator \(\Lambda\), we are concerned with the investigation of the intermediate spaces between A and the domain \(D(\Lambda^ r)\), \(r\in N\), as well as with the characterization ...
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Evaluating the Cosine Function

The Mathematics Teacher, 1971
The cosine function is a mapping of real numbers into real numbers. The function is called cos, and the mapping is usually described with reference to a geometric figure that involves a number circle and a number line. (See fig. 1.)
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Improved sidelobe performance of cosine series functions

IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 1999
The cosine series functions are used extensively for SAW filter design with noniterative techniques. This paper presents improved sidelobe levels of these functions by rigorous application of criteria for minimising the sidelobe peaks. An improvement of 2 dB in sidelobe levels is achieved with respect to the earlier results. A new approach is presented
R G, Kulkarni, S K, Lahiri
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A Functional Equation for the Cosine

Canadian Mathematical Bulletin, 1968
It is known [3], [5] that, the complex-valued solutions of(B)(apart from the trivial solution f(x)≡0) are of the form(C)(D)In case f is a measurable solution of (B), then f is continuous [2], [3] and the corresponding ϕ in (C) is also continuous and ϕ is of the form [1],(E)In this paper, the functional equation(P)where f is a complex-valued, measurable
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Discrete Approximations of Cosine Operator Functions. I

SIAM Journal on Numerical Analysis, 1982
Summary: 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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Application of the cosine function

The Mathematics Teacher, 1963
A project for the trigonometry ...
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On an exponential-cosine functional equation

Periodica Mathematica Hungarica, 1988
Let 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., Singh, H., Vasudeva, H. L.   +2 more
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Cosine radial basis function neural networks

Proceedings of the International Joint Conference on Neural Networks, 2003., 2004
This paper introduces a new family of reformulated radial basis function (RBF) neural networks, which are referred to as cosine RBFs. These RBF models are developed by relaying upon an axiomatic approach proposed for constructing reformulated RBF neural networks suitable for gradient descent learning.
M.M. Randolph-Gips, N.B. Karayiannis
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A Cosine Functional Equation with Restricted Argument

Canadian Mathematical Bulletin, 1974
We 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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PERIODIC AND ALMOST PERIODIC COSINE OPERATOR FUNCTIONS

Mathematics of the USSR-Sbornik, 1983
Translation from Mat. Sb. Nov. Ser. 118(160), 386-398 (Russian) (1982; Zbl 0522.35007).
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