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This paper examines the basic properties of the sum of almost periodic multivalued functions whose values are compact sets of the space R^n. It is much more difficult to prove that the sum of two almost-periodic (a.p.) multi-valued functions is a multi-valued a.p. function. The first proof of this theorem for a single-valued function was given by G.Bohr. Subsequently, Bochner gave others a definition for unambiguous a.p. functions on which the almost-periodicity of the sum follows directly. Subsequently, it turned out that Bochner’s definition is very useful in many other questions of the theory of a.p. functions. Let us now give a definition for multi-valued a.p. functions, according to Bochner, and prove the equivalence of this definition with Bohr’s definition

  • Read count 37
  • Date of publication 01-08-2024
  • Main LanguageIngliz
  • Pages1084-1086
English

This paper examines the basic properties of the sum of almost periodic multivalued functions whose values are compact sets of the space R^n. It is much more difficult to prove that the sum of two almost-periodic (a.p.) multi-valued functions is a multi-valued a.p. function. The first proof of this theorem for a single-valued function was given by G.Bohr. Subsequently, Bochner gave others a definition for unambiguous a.p. functions on which the almost-periodicity of the sum follows directly. Subsequently, it turned out that Bochner’s definition is very useful in many other questions of the theory of a.p. functions. Let us now give a definition for multi-valued a.p. functions, according to Bochner, and prove the equivalence of this definition with Bohr’s definition

№ Name of reference
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