An inverse spectral problem is studied for variable orders differential operators on compact star-type graphs. A uniqueness theorem of recovering potentials from the Weyl matrices is provided. A constructive solution of the inverse problem is obtained.
Пусть для λ 1 задана измеримая 2π-периодическая и существенно ограниченная функция (ядро) k λ = k λ (x). Исследуются условия на вес w(x) и ядра {k λ (t)} λ 1 , при которых семейство операторов свертки {K λ f (x) : K λ f (x) = E f (t)k λ (t − x) dt} λ 1 (E = [−π, π]) равномерно ограничено в весовых пространствах Лебега с переменным показателем-L p(x) 2π,w. Ключевые слова: пространство Лебега с переменным показателем, операторы свертки, условие Дини-Липшица.
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