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This chapter presents a general method for solving inverse source problems using the properties of almost periodic distributions. This method is applicable to a variety of problems, including the dynamics of beams, plates, and spider orb-webs. A necessary condition for source identification is that the sequence of exponents in the almost periodic distribution is uniformly discrete. While it is sometimes possible to decompose a given sequence into a finite number of uniformly discrete sequences, more general methods are required when this is not feasible. A method based on spherical means is presented to address situations where non-uniformly discrete sequences are present.

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Almost Periodic Distributions and the Spherical Mean Method to Solve Inverse Source Problems

  • 章节

  • 发表日期：

    2025年

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  • Alexandre Kawano

摘要

This chapter presents a general method for solving inverse source problems using the properties of almost periodic distributions. This method is applicable to a variety of problems, including the dynamics of beams, plates, and spider orb-webs. A necessary condition for source identification is that the sequence of exponents in the almost periodic distribution is uniformly discrete. While it is sometimes possible to decompose a given sequence into a finite number of uniformly discrete sequences, more general methods are required when this is not feasible. A method based on spherical means is presented to address situations where non-uniformly discrete sequences are present.