Topic
Absolutely integrable function
About: Absolutely integrable function is a research topic. Over the lifetime, 9 publications have been published within this topic receiving 91 citations.
Papers
TL;DR: In this article, it was shown that a continuous integrable function satisfies the initial value problem D q x (t) = f(t, x(t)), lim t!0+ t 1 q x(T) = x 0 (0 < q < 1)
Abstract: It is shown that a continuous, absolutely integrable function satisfies the initial value problem D q x(t) = f(t, x(t)), lim t!0+ t 1 q x(t) = x 0 (0 < q < 1)
14 citations
TL;DR: In this paper, the concept of stability for single-input/single-output linear time-invariant plants is reformulated within the framework of Mikusinski's generalized functions and then characterized; each plant is given by convolution with a generalized function called the impulse response.
Abstract: The concept of stability for single-input/single-output linear time-invariant plants is reformulated within the framework of Mikusinski's generalized functions and then characterized; each plant is given by convolution with a generalized function called the impulse response. The impulse response of a stable plant is the generalized derivative of a function of bounded variation, and is therefore the sum of three uniquely determined functions: the first being an absolutely integrable function, the second being an absolutely convergent sum of at most countably many delays, and the third being an atomless singular measure, a stochastic phenomenon. >
13 citations
TL;DR: In this paper, the real solutions of the differential equation y prime + (1 + f + h cos 2nx) y = 0 where f(x) is an integrable function, h(x), is a function of bounded variation and n is a positive constant.
6 citations
TL;DR: In this paper, a boundedness theorem for the real line is presented for the continuous integrable real line problem, where the integrability of a continuous integral function over a real line has been shown to be bounded.
Abstract: In this note we present a boundedness theorem to the equation
x ″ + c ( t , x , x ′ ) + a ( t ) b ( x ) = e ( t ) where e ( t ) is a continuous absolutely integrable function over the
nonnegative real line. We then extend the result to the equation x ″ + c ( t , x , x ′ ) + a ( t , x ) = e ( t ) . The
first theorem provides the motivation for the second theorem. Also, an example illustrating the theory is
then given.
6 citations
Posted Content•
TL;DR: In this article, a Fourier approximation can capture the variation in any integrable function of time, and it is possible to use successive applications of the test to "back-out" the form of the time-varying intercept.
Abstract: The paper develops a simple method that can be used to test for a time-varying intercept and to approximate its form. The test is solidly grounded in asymptotic theory and has good small-sample properties. The methodology is based on the fact that a Fourier approximation can capture the variation in any absolutely integrable function of time. As such, it is possible to use successive applications of the test to "back-out" the form of the time-varying intercept. We illustrate the methodology using an extended example concerning the demand for money.
5 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2015 | 1 |
| 2006 | 1 |
| 2003 | 1 |
| 2001 | 3 |
| 1995 | 1 |
| 1988 | 1 |