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Bounded Cosine Functions Close to Continuous Scalar Bounded Cosine Functions [PDF]

Integral Equations and Operator Theory, 2016
Let $(C(t))\_{t \in R}$ be a cosine function in a unital Banach algebra. We show that if $sup\_{t\in R}\Vert C(t)-cos(t)\Vert \textless{} 2$ for some continuous scalar bounded cosine function $(c(t))\_{t\in \R},$ then the closed subalgebra generated by $(C(t))\_{t\in R}$ is isomorphic to $\C^k$ for some positive integer $k.$ If, further, $sup\_{t\in \R}
ESTERLE, Jean, J. Esterle
core   +4 more sources

On a subfamily of starlike functions related to hyperbolic cosine function

Journal of Analysis, 2023
We introduce and study a new Ma-Minda subclass of starlike functions $\mathcal{S}^*_{\varrho},$ defined as $$\mathcal{S}^{*}_{\varrho}:=\left\{f\in\mathcal{A}:\frac{zf'(z)}{f(z)} \prec \cosh \sqrt{z}=:\varrho(z), z\in\mathbb{D} \right\},$$ associated with an analytic univalent function $\cosh \sqrt{z},$ where we choose the branch of the square root ...
Mundalia, Mridula, Kumar, S. Sivaprasad
exaly   +4 more sources

Dual-Channel Cosine Function Based ITD Estimation for Robust Speech Separation. [PDF]

Sensors (Basel), 2017
Li X, Ding Z, Li W, Liao Q.
europepmc   +2 more sources

RELATIONS BETWEEN DISTRIBUTION COSINE FUNCTIONS AND ALMOST-DISTRIBUTION COSINE FUNCTIONS [PDF]

Taiwanese Journal of Mathematics, 2007
In this paper, we give connections between distribution cosine functions (defined in [10]) and almost-distribution cosine functions (introduced in [13]). We prove several equalities involving trigonometric convolution products and distribution cosine functions as well as some relations between distribution cosine functions and ultradistribution ...
Kostić, Marko, Miana, Pedro J.
openaire   +4 more sources

Almost-distribution cosine functions and integrated cosine functions [PDF]

Studia Mathematica, 2005
Operator valued cosine functions were introduced in the 1950s to solve well-posed abstract second order Cauchy problems. Later, in analogy to operator semigroup theory, the strong continuity conditions were weakened to be able to treat also ill-posed problems.
openaire   +1 more source

The Cosine-Sine Functional Equation on Semigroups [PDF]

Annales Mathematicae Silesianae, 2021
Abstract The primary object of study is the “cosine-sine” functional equation f ( xy ) = f ( x ) g (
openaire   +3 more sources

Integrated cosine functions [PDF]

International Journal of Mathematics and Mathematical Sciences, 1994
In order to the second order Cauchy problem (CP2) : x″(t) = Ax(t), x(0) = x ∈ D(An), x″(0) = y ∈ D(Am) on a Banach space, Arendt and Kellermann recently introduced the integrated cosine function. This paper is concerned with its basic theory, which contain some properties, perturbation and approximation theorems, the relationship to analytic integrated
openaire   +3 more sources

On the Spectrum of Cosine Functions

Journal of Mathematical Analysis and Applications, 1999
The author gives some characterizations of the resolvent set \(\rho(A)\) of the generator \(A\) of a strongly continuous cosine function \(C(t)\) with the aid of the equation \[ u''(t)=Au(t)+f(t). \] One of these theorems shows that \(1\in\rho(C(1))\) if and only if, for every \(1\)-periodic function \(f\in C([0,1],X)\) (\(X\) is a Banach space), the ...
openaire   +1 more source

ON GENERALIZED SINE AND COSINE FUNCTIONS

Demonstratio Mathematica, 1995
The author finds addition formulas for functions \(f\), \(g\) which satisfy the functional equation \((f (x))^n+ (g (x))^n =1\), where \(f\), \(g\) are supposed to be real functions on a given group \((X, +)\) and \(n\in \mathbb{N}\) is fixed. The obtained addition formulas coincide with the well known representations of \(\cos (x+y)\) and \(\sin (x+y)\
openaire   +2 more sources

Riemann-Liouville Fractional Cosine Functions

Electronic Journal of Differential Equations, 2015
In this paper, a new notion, named Riemann-Liouville fractional cosine function is presented. It is proved that a Riemann-Liouville $α$-order fractional cosine function is equivalent to Riemann-Liouville $α$-order fractional resolvents introduced in [Z.D. Mei, J.G. Peng, Y. Zhang, Math. Nachr. 288, No. 7, 784-797 (2015)].
Zhan-Dong Mei, Ji-Gen Peng
openaire   +4 more sources