Литература
Колмогоров А.Н., Фомин С.В. Элементы теории функции и функционального анализа.- М.: Наука, 1980.
УДК 517.929
ОБ АНТИПЕРИОДИЧЕСКОЙ ЗАДАЧЕ ДЛЯ УРАВНЕНИЯ ПЕРВОГО ПОРЯДКА С ОТКЛОНЯЮЩИМСЯ АРГУМЕНТОМ
Борбасова А.Т.
Южно-Казахстанский Государственный Университет им. М.Ауезова, г. Шымкент,
Научный руководитель – д.ф.-м.н., доцент Шалданбаев А.Ш.
Введение
В работе [1] изучены спектральные свойства краевой задачи
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGUAAAANCAYAAACw26D4AAAACXBIWXMAAA66AAAPKQFOEYU8AAAFyElEQVR4nO1XaVBTVxT+ICBCDJAQxACRUiMuBNnc2ETBBRRXUBlEcBBZRcVWHGgFK+JCRxmoI4KOdaFWwYWx0OICFUeMIqAsFQSRopbIIosYFjGhLw8KfQYt/ILO+M3cmfvOueecd+9377nnKkgkkm58xoiCwnD/wKAgFkFwKwMvO7SxeokFRSWqKULS9T+wwMEJX45jDMltV6sQmTmFYGjqwsqc/9FxFY+ycOdhE9Z4OINO65dL2ptw5nwSjCycYT5Ze0ixP4X/BSmVd7PwqFYL/m4WJEGn4w7iweMazAuMgrPJNLjZduHwsRQEhnuBLU+1vX3rKgxnOEKDrkhVEH6O740F3WYObh6NBy3ie8weryITW645HxfS6hEcupYkpLP1NbJ++wlc+0DwNZjwcHXHgZ1HoHYwDDxlmoz9p5CXfhIJ10owycweX29Y0icf+aSIG3EtLQdzQqLIT2HeWQjajXFo/0p4+BzAzOOR4Oqbw0znCrKLagmStCjmwppqTBDLuu0U5qFEbIijTosRnZsBRdoAgwikHTkLM9cokhBRSzVO/XwZgtQs+M7YCIJpyCsz4eqkjDPXKrB7xeRBT6vzZTbOZlZiT2QYErduw9WZFlg2lUXqhpWUp1knsHC+Dxwjj4FW+gA+sccQs1wRjOBihOg9hMXmBKQkxqG0hYM1zJ5dWF1SDGtHYpHY6jDUi0JdRze4hFybOR7ZFULgA1I+hsqCXzHOIQAvb8egsHk6AonUlxA8HT8q+iNrhxWcl1pjcfQD1JWPgqfOaNKGrqaHwE2eeF+QR/E1YaIRniZWAv+QQpzCOH97bDuRSxnne+Ie4r1mkv3Xr16AM20WOGpszLVjIaeqbvhJqS1MRYKgGw/bGnBqSxDkffaCr96BuNR8hH/zO0ZH2OLgtzHga3ZDwlWGcm85UvukGSJ+l4w/RXUFtD0mSIFJT2raF4aSBqD8SSGu3y7HGBYHHoFBMNdhkPrsG2Is/04TZZfewMrRAXSI4LXnFzSFxKMGK+HunwiX2drYkdoNdSVqWpJIlMBQ+Vc6ZLJBr70BkXhJz51Do2P5lhgYrGqh2HH5k/r6b+pbUF+rPODaDBspz0uqMNnQDhJhGUpGayHUgE1Ohs40gLzqUeQW8WBlYQ0lOSEU69vRLkfsVMLuCxNd3CwlduV0GrppY8HqXbCu5vdQ4XB6nBN+Nu2KJbsXzv0Aayc/6Kj2L2JX2xsUyEngoaYChh4d6c9rCUqmgE5cKeMNmnHn/iMYzZoNpVFKUH8LNHeKwf7gvmhtk26MUWRf3NII8bgplCLgv8DS5qL+VjlBJNDYKIGBsSaZHsWiruEjhclhICNhH9prTImzLEJqej58N8wlJkaHJpEtGqAPrsYYYsYa4DP+QrWwFWxil/MdvPHaLxhbbnLAddqIscyey/lF/TPwbF0GFftd5ysoN7YibPtWNLQ0Y3uUb++C0qGro4vLZR1Y7ahNnigbg3d4XNUCnjS1EPfb6ehoXLl3H4JD+6ESupM8ec+K74Fn40aJoce3INrH/4FtYANj+Uvw2xQIDR1T7OKpojQlHEXJ8cNHCs/OGylEIxFA1U01t8S8Bb1HncaCqTEPmYI/Ye5iRHxOxLnkNMp4cWMFMgs5iPBlDSp2a3kF5GZ4InartYxOncWGt/2iPpIWOi/GukQB7PdKUxMLnqEHyNYfnKgGk1ux/qT+IGfeA2mB8NX+0xRZbrkWyjIcRlb1VXX3PM7kd2CzlzslFZi7+ECVeCukpAtk3iltwgIk57zC7kMB0PigHJZirVuQjKyu7S1clplSZE1Vd3H84h0sdffDFI3+4N36ixAXVIzUpMtY4b5K5p2SdPESvA7vhr7CAMGHCJOdAZgTGT6ySNG3dEWE5cC6iSZ2RJOVq3DMsGFwWasP0+Z7yciY+pYI2TFwcJa2EdZ5GsnIpbvdY7330IJ/AtJKTIoRRcpn9OAzKSMQfwPSf/PWCgaNRAAAAABJRU5ErkJggg==)
где ![](data:image/png;base64,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) -комплексные числа, -спектральный параметр.
В настоящей заметке мы рассмотрим более широкий класс уравнений, но с менее общим краевым условием:
![](data:image/png;base64,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) , (1.1)
![](data:image/png;base64,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) , (1.2)
где -вещественная величина из полуинтервала ![](data:image/png;base64,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) , а -спектральный параметр. В частности, при ![](data:image/png;base64,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) наши результаты совпадают с соответствующими результатами работы [1], а отличие состоит в том, что появляется дополнительный спектр и собственные функций соответствующие этим дополнительным собственным значениям не полны в пространстве ![](data:image/png;base64,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) , хотя собственные функций соответствующие к основной серии образуют (после нормировки) ортонормальный базис пространства ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAANCAYAAADMvbwhAAAACXBIWXMAAA75AAAPKQHH3f3+AAADa0lEQVR4nM2Uf0yUdRzHX3eewHPe+YTc8cuBoDBE49Ss+JGcMZ1hY6W2puWmLHcVq9GMNnBZK1uNrdCV/sH44eYfZytUaJMfS5kGjSGt7AccFqBwC7jz7gQP4cj0rofn9OjGteFaW+/t2fP9Ps9nn+/r8+P7UXm9Xh//A6lCfRz+vpMelwdrUw0rSk6Sl+Bn9XqcdPeNYTCk/uuDrX2XUcSlk6CJmAXprD/M0eYhyt4vJyNOYOn6LCIdVznteBKDzg8x4bZx4vNGHss2yvvLTbVUNv6ILnktb762jyiBAGyduYq2X2wsScuhtGgXGkUIkj/H+brSzOO7XyQ5VvCD6CM1hItpMoTsbHyAxo4feMK4kZFxD1FhXr47VUXMykIyDYncGrxI5anfOPjZx7SU7aW6zUjZU/4sOYcsxGe/wtEXbnNoXyEXN22jIC1iDkfiqjyeUXr4oPYk4ubtfpCx4T9Y/0hOwKiroZail8q5oVBwts9LhmeAzm+97Ny1TPrrw2HtZWlurpzWLc+u5t3uPrgHEr3SSPRMMJOjqMMiWKQWGO2qZkPBy1xzzaam/CsLb+Wtw2Nv49ihBgnk7iQdV35i9d7CgFFW4Uc4pccvH54hO/1xcWhVd6W9EvfoDRy2mKAIb0kVvF+CmfKYG86SUlwh99eEWMCxI5+yJHM7dcdrOPDOe3IpZ+wyJhzktrSj8k0Oct2exI54LVPDl2gbTSL/0eBD7ku9UCm/9UnLsHf1c/22F9vITdJTEtF4J3G57xC1WEVz63n0a58mS7TR3uNiQ4KL3l4tz20aIyxCKtP0TRBElGFCwLeq9Yvj1FuuMHagGGe3hT01jXMAwsVo9CMu7B4FGrWPWEM+mfVvsP/1/QiqWMo+TMNuOU9F0wBF2Qv45Egrqx7uoM55jfxSMz83N/B7cg6RvmkcHe18s3ErW4xrUE+76VHqaE+XemSzqYIeU8gEBKTUxrImtZ/BETcrUrQoBR0l5eYgG+uvd1iuzSBZavALrUXBDgxvc/jesrplNtCpcSvhMQL5Jc+HniNztGAR20wHqTrzJZopo3Rz5s6RyHQjr2aJ83Ing1sucK7pKqbi0tnrOx+p9csp3rNYHmihpBXnDyFr4UNsNe0mXvzbQJuvZkpiMOge7MB/UGLquqD9A4H8l/oLDiMtqn5v+iQAAAAASUVORK5CYII=) .
Из теории Гильберта-Шмидта известно [2], что самосопряженный и вполне непрерывный оператор имеет полную и ортогональную систему собственных векторов и других собственных векторов он не имеет. Не вполне непрерывный, но самосопряженный оператор может иметь полную ортогональную систему собственных векторов и соответствующих им вещественных собственных значений. Спектр такого оператора состоит из собственных значений и предельного спектра, являющегося предельными точками множества собственных значений. Спектр, изученной нами задачи (1.1)-(1.2) резко отличается от спектра выше упомянутого класса операторов и в этом состоит особенность этой задачи.
Вспомогательные предложения
ОПРЕДЕЛЕНИЕ 2.1 [3]. Система элементов ![](data:image/png;base64,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) , ![](data:image/png;base64,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) называется
базисом гильбертова пространства , если каждый элемент ![](data:image/png;base64,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) представим единственным образом в виде сходящегося ряда
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADgAAAANCAYAAAD8Ma0AAAAACXBIWXMAAA6uAAAPKQHWVsWxAAAER0lEQVR4nN2VD0yUdRjHP3DHcceBcAcISMoBwlAyOFDB0CksBJECVMRohRptJJTEYhFsOlsTyKmJqZmOlstwikiNpnPan0kuc4ChBAzQyTT+qgfIn5PjrveOQtAoEtpa3+3d+77P8/ye5/n+nuf3/MR6vd7A/xjiyToY6r9DQc6rFFeLCJz7lEmmvddMr0c0n2XF8n35ZVy8/NB1NnFbZ0tk8LxJJ/1PMGmCIpk9iS+/xMn0MjZmv4+/sw09LZcpOFFN1Y+XaO9+QGNRHjckgQQ6Gajx8sTX3moqcp8QJk3QCCd1PO/EfcW7efs5mpuJ0mUBOW8uoKnyNFfKzqGzskP6oIFzd6wIWGkxFSEnDLGZ/jYbPFfis/tzQrv2sL06jFM7XzQpjZWIXRTEt82jVkhsyDxygfy1z4xxFJ2ylaNuMXwRtYq05V4mmWfACvKE50nQVnWC5REJ1HVHUKs9g4fh8VFRtC8F54BVbE2IpMUvjaqSPVhbmI0lqO23Y9f5vbyW9QHP5u/iVJLDiNLGaS75n5bRqTV/uMJMhLuf+2PBzCQuLNsYj72j7IkIjUZz+WF2l1vy3a0hzLVd2D5CzliUjE25rE9PpfRgCQeq7nM8ZwsNPf2olWPbXyyRy2ntaEU8aINimhX3Bw0juzCkHZhwUpeKdiMPXkO8enjQdPVo0LdVcrikheT0RBQSM3o6W2jT9Jr0IrEcd5ULA5oOzpZ8jXXQCsJ8nUy6poqbBMxPQiHuo7tPxL3Gb/ik9C6pm1cP59bTysB9D6z6bjHoPRvXrgpadVLcZFLKj+2g2eF5Ep/zGSZY/FE2elUEMYsH2ZZ3gPys17H+fQgYB8j80Ki/JWdM4LR+Dm9H+Zr+NdcvkHfkJ3KzYlDIBrny5Yc0SYNYrOziXGWjyUZqo2J1YjT9N2qorGhA7b1sxJ/nPDcOFuZy9awXUYnrCPVxFfzouXh8B62O4bwiJO+l+JjsrJP8qlPS1+BPwltvoJSZ4zDzabq677J/22bq7ggE16RtH/YavZR1E67XQxiviayMDA6VVfNe0kP50pQddF+vResjVKnenNANIXjKDfiEjF2vUC8jXN1I5yjZrLBkjgnPH2gVzuOgtzvaOhkhsQFgbiB97yG8i/bR6xMz0jVGtHc2YDFjCdKZofivj5uCa8JSypaCYjJ3jZXLlDO4WlqIxUANZzokuAm72q4RWq6/f3id0KKOrs6Iem5SWXsNjVbBksBZpio8il8u3sLCrInzGhs8BT/IFaDvRSSCQJXTiJ3xbNZe7EU3rZC7LnEsqP95Cq4Jczmuqtl/Tj48FrXCmupr9cgklky3VzD9ERsjXd/ISPQS63FDzHkhnoWCn5qaOmwtLUfiRqxNHWNnwI7ITcko5Tp+qG037vLU3IPjwXnmcOssCg4a10amVBEWrpqQn4VBwX8dUCDt5iY3fUYucTG9/1WC/wX8Bvcga4mGFL+CAAAAAElFTkSuQmCC) . (2.1)
Если, кроме того, выполняются равенства
![](data:image/png;base64,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) , ![](data:image/png;base64,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) (2.2)
то базис ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAANCAYAAACkTj4ZAAAACXBIWXMAAA7+AAAPKQHa2M1GAAACHklEQVR4nK2SXUiTYRTHf6971z5am0vdZORmVoYOxFGMCgxvWpKpFEKKBWUFgY3lhalFF6EQFGEfhBbKpDLoE+xKzC7qQroRSU0roygq0pkjl80s3qdtlkJ2sYv+cB4OD+f5necc/rKiCMF/kBw9hnv8tHQNUFRZx5Zsa1wP+7vbaLv7lIr6U6x16CIgMU7ntYeUn7zMxvSlcf/A5dmPT77I2ZZbrKrYhyz9DDH9Q0OyKX7IH5ms6ZgI/h5NtmLJUPgaDoNZF7tsP3+AjPUl1O8qZnydj8HOJrRIi0DTHwKEbWtw50RAj+51oEorxG5WI8Kv8B65gK/GS8el+7T2B7lxvJGRYBiXWb8IZM3dhLPnKr17byNv3rmDJ4eP8i5YiDHhE8psJqrgS4Qzi+WhIcaFHrt2Cb03z/A6cRu7tzrnQRPP+3iRnE/+CQ+ymJliKqjCoNOhTszEoW6jrn6YMSmVbyO5lFZXkaSTSV6Zw+TnLzQ3etlQeRqXTYc2yYg68J5no5HRErR6lqlUcy0kC7VX/NxpP4fGXUZRdupC9zcDqFd70FjyYpColJkQge8hRCgCEpKNPTWlNDfV4i6rpjjLgFajwpWWMg+RxEcG+2ZRRlsZSy1hUii8feDnetcUxxoOscIk5gxpy/HQEImoojbfXu79a61GCqoOkmKc4fHQBHpJivnI5VmokOPxi5AMOByGWF6QZ/9nTVygePQLDbGmJfHzDfgAAAAASUVORK5CYII=) называется ортонормальным (или ортонормированным).
Примером ортонормированного базиса в вещественном пространстве ![](data:image/png;base64,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) является тригонометрическая система
![](data:image/png;base64,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) (2.3)
Пусть ![](data:image/png;base64,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) - произвольный ортонормированный базис пространства и -некоторый линейный ограниченный обратимый оператор. Тогда для любого вектора ![](data:image/png;base64,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)
![](data:image/png;base64,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) ,
и следовательно,
![](data:image/png;base64,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) ,
где
![](data:image/png;base64,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) , ![](data:image/png;base64,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) , ![](data:image/png;base64,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) . (2.4)
Очевидно,
![](data:image/png;base64,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) , (![](data:image/png;base64,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) ).
Поэтому, если
![](data:image/png;base64,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) , (2.5)
то
![](data:image/png;base64,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) ,
т.е. разложение (2.5) единственно.
Таким образом, всякий ограниченный обратимый оператор преобразует любой ортонормированный базис в некоторый другой базис пространства ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA8UAAAPKQHLcP4WAAAA7ElEQVR4nGP59+/ffwYiAQuxCuGKD65oZ5h/8jtDbU0Fw/cDixiaV15hKO/vZDCS5sZULM7HySCjbsigLMzF8E1HnIFp538GDXFu7CZfufyVQcNOEyxw5dA2BinfCgYuLA5kYWT8wPDgxR0GfZbvDLevX2BYve8vQ9RURexu/v3sKsPdX8YMSYaaDBzvrzDc5uZnMBZiAku+efGCgUtEAm4Ly9p5ExgOPpdiePfpPcP9hbMYLhy6x/DwGyODAsN9hva8MoaAzgUMtopcEMXh1asZwqHWqJRMZHhQAmL9B0IFht5VqzA9SCwYJIoBMhtKVZBFAMwAAAAASUVORK5CYII=) Базис ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAANCAYAAACkTj4ZAAAACXBIWXMAAA54AAAPKQESMTqDAAACOUlEQVR4nK2SX0jTURzFP87f/jtna7pJ/skgxRJ6sCxm+VBRGGxpGUkObSYZhQoGQYWBJSIYRuQ/6ikSejCosJ6CXtaDBUElmBgLC8HcFLXZ5m/pfv3mxBSRfOjAvQ+Xc8/9nnOuEA6HJf4DhMj24WUXD9xjuC7Wszst4Z+Xfk9/525bJ/PW/dRU29HHSggxC5M8ffyOS7c72GHVLZP9X930jpqpLMheI6RMSKP+Sh1N1bUMnbaTuzky0cI0QfQY4/Qy5a/L4Tf9aNKL150qVqsiOd66wprSijk1xJwo4h19xfF9TbR7+nn7cYrMA2Fayyuw3ewif6tuldBCMMTAryQKzdH3hde9PRgzHSTGxSKEsymqKsJqnGCCME6zifHtSRgN2rUT6eMpO5HBk+4+NLtsCAdPluCuuYrPcYRkmTCo9JPoHWBcyMP3zYPHZMOumqT92h2ONTSzTRu1HwqKvHg+jKvz1uLZYkazP1Vo1GqUigTypRHOXm5maNZCR18BVa4yjLogmyw5iJ+f0fY+QHXlGeLUEhlaHz4/slAkI1nAoFBE29CZON/SQ3pDOYHS+xTv1ETzmJ1hXI4o9GWMvKPOxbpDgRhmxB+IoaWwJSmFirrD3GttpORcLXtSlUxl2TmUqVrOY9o3wvzYJI8+DWDPKiSg9dLd9RCT4zoFKdJSazLSch20yIulD1DqPLUqWIMli7ILOcx5B/Hr9egSzdTfaFzFEdb9KCsQsbwl0n7S3nU5GxLaCP4AJ7i0TicspRsAAAAASUVORK5CYII=) , ![](data:image/png;base64,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) пространства , получаемый из ортонормированного базиса с помощью такого преобразования, называется базисом, эквивалентным ортонормированному (по терминологии Н.К.Бари [4] –базисом Рисса).
Достарыңызбен бөлісу: |