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The convergence rate for Schr\"{o}dinger operators with complex time

Yaoming Niu|Ying Xue|Tie Li
대한수학회 (The Korean Mathematical Society)|2024.11|대한수학회지 (Journal of the KMS)|제61권 제6호|pp. 1145-1170|DOI 10.4134/JKMS.j230461

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키워드

maximal operatorglobal estimateSchr\"{o}dinger operatorcomplex timelocal estimate
주제분류수학

초록

In this paper, in one spatial dimension, we study the convergence rate for Schr\"{o}dinger operators with complex time $P_{a,\gamma}^{t}$, which is defined by $$P_{a,\gamma}^{t}f(x)=S_{a}^{t+it^{\gamma}}f(x) =\int_{\mathbb{R}} e^{ix\xi}e^{it|\xi|^{a}}e^{-t^{\gamma}|\xi|^{a}} \hat{f}(\xi)d\xi,$$ where $\gamma>0$ and $a>0.$ The convergence rate for Schr\"{o}dinger operators with complex time is different from that of classical Schr\"{o}dinger operators in Cao-Fan-Wang (Illinois J. Math. 62: 365--380, 2018).

Abstract

In this paper, in one spatial dimension, we study the convergence rate for Schr\"{o}dinger operators with complex time $P_{a,\gamma}^{t}$, which is defined by $$P_{a,\gamma}^{t}f(x)=S_{a}^{t+it^{\gamma}}f(x) =\int_{\mathbb{R}} e^{ix\xi}e^{it|\xi|^{a}}e^{-t^{\gamma}|\xi|^{a}} \hat{f}(\xi)d\xi,$$ where $\gamma>0$ and $a>0.$ The convergence rate for Schr\"{o}dinger operators with complex time is different from that of classical Schr\"{o}dinger operators in Cao-Fan-Wang (Illinois J. Math. 62: 365--380, 2018).

참고문헌 (25)

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