On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the Infinite-Dimensional Case

Автор(и)

  • V. M. Bruk Saratov State Technical University, 77 Politekhnicheskaya Str., Saratov 410054, Russia

DOI:

https://doi.org/10.15407/mag10.02.163

Ключові слова:

гільбертів простір, лінійне відношення, інтегральне рівняння, характеристичний оператор, неванліннівська міра

Анотація

Визначено сімейства максимальних і мінімальних відношень, що породжені інтегральним рівнянням з неванліннівською операторною мірою в нескінченновимірному випадку й доведено, що ці сімейства голоморфні. Показано, що якщо звуження максимальних відношень неперервно оборотні, то оператори, обернені до таких звужень, є інтегральними. Використовуючи ці результати, доводимо існування характеристичного оператора й описуємо сімейства лінійних відношень, що породжують характеристичний оператор.

Mathematics Subject Classification: 47A06, 47A10, 34B27.

Посилання

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Bruk, V. M. On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the Infinite-Dimensional Case. Журн. мат. фіз. анал. геом. 2014, 10, 163-188.

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