2003, 2003(Special): 709-716. doi: 10.3934/proc.2003.2003.709

Analytic continuation into the future

1. 

Department of Mathematics, East Carolina University, Greenville, NC 27858, United States, United States

Received  September 2002 Revised  March 2003 Published  April 2003

A class of analytic advanced and delayed differential equations, which are defined in a neighborhood of an initial point, and which are assumed to have formal solutions in terms of power series, is studied. We provide growth conditions whereby the (perhaps non-convergent) formal series solutions can be extended to analytic solutions defined on a sectorial domain with vertex at the initial point. By introducing a new Laplace-Borel kernel, and obtaining estimates on its decay rate, the concept of a Gevrey series is generalized. The class of equations studied includes advanced and delayed initial value problems with polynomial coefficients. Key estimates are shown and an example of a new application is given.
Citation: David W. Pravica, Michael J. Spurr. Analytic continuation into the future. Conference Publications, 2003, 2003 (Special) : 709-716. doi: 10.3934/proc.2003.2003.709
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