What is the Laplace Transform?

Widder, D. V.

doi:10.1080/00029890.1945.11991601

Cited by 146 publications

(188 citation statements)

References 2 publications

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“…For instance, M. E. Muldoon [39] showed how the notation of complete monotonicity can be used to characterize the gamma function. An interesting exposition of the main results on completely monotonic functions is given in [48].…”

mentioning

confidence: 99%

On some inequalities for the gamma and psi functions

1997

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confidence: 99%

On some inequalities for the gamma and psi functions

1997

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“…where s 2 C is the Laplace variable [12]. Furthermore, the Laplace transform of the response signals d 1 (s) and d 2 (s) is related to the Laplace transform of the load vector p(s) 2 C np through the transfer function matrices H 1 (s) 2 C 1⇥np and H 2 (s) 2 C 1⇥np , respectively, as given by the following equation:…”

Section: Mathematical Backgroundmentioning

confidence: 99%

“…The transmissibility function T 0 (s) is related to the transmissibility function T (s) as follows [12]:…”

Section: Mathematical Backgroundmentioning

confidence: 99%

Synchronization of Data Acquisition Systems for the Purpose of Structural Health Monitoring

Maes¹,

Reynders²,

Rezayat³

et al. 2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. This paper presents a technique for offline time synchronization of data acquisition systems for linear structures with proportional damping. The technique can be applied when direct synchronization of data acquisition systems is impossible or not sufficiently accurate, for example when multiple measurement nodes with different clock signals are embedded in a health monitoring network. The synchronization is based on the acquired dynamic response of the structure only, and does not require the acquisition of a shared sensor signal or a trigger signal. The time delay is identified from the spurious phase shift of the mode shape components that are obtained from system identification. A demonstration for a laboratory experiment on a cantilever steel beam shows that the proposed methodology can be used for accurate time synchronization, resulting in a significant improvement of the accuracy of the identified mode shapes.

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“…In particular, given an exponentially convex function L(t) the function ln L(t) is convex. This class was introduced and extensively studied by S. Bernstein [5] and D. Widder [30] in connection with the so-called completely (or absolutely) monotonic analytic functions (see the definition in Section 3.2). We only mention a deep penetration of the both classes into complex analysis, inequalities analysis [2], special functions [25], probability theory [19], radial-function interpolation [29], harmonic analysis on semigroups [3] (for further discussion and references, see recent survey [4]).…”

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confidence: 99%

Length functions of lemniscates

Kuznetsova

Tkachev²

2003

manuscripta mathematica

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Abstract. We study metric and analytic properties of generalized lemniscates Et(f ) = {z ∈ C : ln |f (z)| = t}, where f is an analytic function. Our main result states that the length function |Et(f )| is a bilateral Laplace transform of a certain positive measure. In particular, the function ln |Et(f )| is convex on any interval free of critical points of ln |f |. As another application we deduce explicit formulae of the length function in some special cases.

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What is the Laplace Transform?

Cited by 146 publications

References 2 publications

On some inequalities for the gamma and psi functions

On some inequalities for the gamma and psi functions

Synchronization of Data Acquisition Systems for the Purpose of Structural Health Monitoring

Length functions of lemniscates

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