多维矩问题中的唯一性问题及其在相空间可观量中的应用
The uniqueness question in the multidimensional moment problem with applications to phase space observables
摘要：
应用多复变全纯函数理论证明了经典矩量问题的一个涉及指数有界性准则的定理的多维变式。本文将Petersen关于多维矩量问题与一维矩量问题之间关系的一个定理推广到半直线和实直线的紧子集上。这些结果被用来解决由数态产生的量子相空间可观量的矩问题。
英文摘要：
The theory of holomorphic functions of several complex variables is applied in proving a multidimensional variant of a theorem involving an exponential boundedness criterion for the classical moment problem. A theorem of Petersen concerning the relation between the multidimensional and one-dimensional moment problems is extended for half-lines and compact subsets of the real line. These results are used to solve the moment problem for the quantum phase space observables generated by the number states.
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