СЛЕДСТВИЕ 2.3. Система функции ![](data:image/png;base64,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) образует ортонормированный базис пространства ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABwAAAALCAYAAABs3u23AAAACXBIWXMAAA7XAAAORgEZ3ITnAAACoUlEQVR4nL2Sa0jTYRTGf86tbFvbmk3zUl5m826rZEWpfTBB1LLsZlkkQkURVHSFTPJDBkHpRz9EQRFdbAQapBmBGkSUSbOamNW0IGu63LyxmlvzP5hFFH2QHnhfzvtyznnOec4Ru91uDz8hwGWjbFksRkcCDY3NZGpnM50QT17Gs8Vc7Eyg7upp5GI1ta1vWNP0iDkSl+B0/1oVI9GbWLt0Hg21F3jwxcHQgJJz1aeIkAX8lcDcfIu6DwoqynKnCFWhaeQvWoc8EL6PWjl79DBWaTIzY1NJVfbQZIqgsnghw72PuNU1wfXa81wpL+VOi5n9eUn+5M+ajZj7x/xv7fJcVmYXkFxznOa32eRoJT7CV729pGdqBKcZs2TsOHgSpzsQTeR83j68hMRQKhTzcfgjwbIFgl9kXDjt9m/+5Lb3HViHbPQ4glglM3PPvZrVGjke0SzioiOo7+wmNiYFcYD9KX0OLRvC5zJm+4RbGUaMLt6fyOocR6WSC7ZIJGHAYRPsMasdsU7i91PHLCbE9Bp9WiL9d19SeCSLMJXQD1KZAqf9u09SS3s7FkkQH0wtXL7ZxuaqCnTSqT1akJhOX5MZcsIJDklF47yNsaWV1ndidm5V0lBzhojicpaGjPL4xRPSNxqoH57AZXpORrZByGGxdDFPV0Cox4PYpU5i+/JB+j99Rb+l6BeySciS1pNSX827wQxiQ3VUVh6jtcPCtgMnSAwaoa13gngFfBsfZUVuKTptFKrSQkYUPumdn7tpt0VRtCzKOxYvoVafhVb/5y3ziKQUb83DaLzEWEEJKV7p1nmPIKt3BPmH9hAnFKlhicG3BwmGTP9cbzSaKCgp8zci/jPVFCbns2v34t/+peow4tR/j9u399e4fyKcTvx3wh8cmt/OKCX7WgAAAABJRU5ErkJggg==) .
Это следствие играет наводящую роль во всем дальнейшем.
Основные результаты
ТЕОРЕМА 3.1.
(а) Если - вещественная величина, то каждое решение уравнения
![](data:image/png;base64,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) (3.1)
является решением уравнения Штурма-Лиувилля
![](data:image/png;base64,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) (3.2)
(б) Пространство решений уравнения (3.1) является одномерным;
(в) Общее решение уравнения (3.1) имеет следующий вид
![](data:image/png;base64,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) (3.3)
где произвольная постоянная.
ТЕОРЕМА 3.2.
(а) Если ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACMAAAALCAYAAAD1JjQCAAAACXBIWXMAAA6TAAAORgGNFcydAAACVUlEQVR4nO2SXUjTURjGf1v/zTF1bm5lipa6jDAV20QxNWkuSytKFkYXURGYXVQG0UUXSYI3lfRhmlZ4IQSRBkKlJH5UM5NsjjAlLYyaXYTpTfk52Zou3JYVdBNe9MB7Lp73Oec85zmv4HA4nCwRCHOLtb2Ozv5JNuftIjYs6J8aGHzWhVqfglomQvjW10D10ykKMpZRVl7L1dLj+It9wxLZx2hpbsP2YZZth/ex0u/vwpz+8p67jWbkinWYdifPc46JUR7UVXH5+iA3n6eixonQ3dpMjP4k+lQJy2tLGByBDSHuQ6Y+D9DU2Uvf0DBpGVvYsUmLxsvIyJtWym+14JQGoFaIic8/Sla0cqE/0N2O5XUfbyeD2GvIJGJtpIt17xdLZaRnmWh7VLGgF+zTMyj8A8APAgWv58yO03SvAZt8DYUFhWgCZYvSKq+oJ+dEKdLuS1QPJVLkZWR0qIcnHV2odDspzoz7wXolKvijVqkQiaQeSh0eyv3+fsZjFNiE1YQqPWKjaQ8vXlqpulGFTp9GYsJ6woLl7v6EjSlnHFEr7NyxfGKr6RDjDtHCF6ujdWQb7Vh7OzhXaSU3OYlYXeyiEXA6ZzxmEnKOoCo+w6kLGjbmH/SZh8AQLVnbtRizxzCbu3hc/xDDgXy3Rh5BmMxC5TUp0as0vOqxYkzSuvL3XBQZnzJfua6ZaTRb+Dj81WdmbtdU825kgLLT51FKFAgSZTglV2r5E5ySYNINuWDwRD3HFV2s+Vn5y/1+mijy8qJ8OLFczf5jZ13l4QSWEP6b+R2+A7gXwTB47LmpAAAAAElFTkSuQmCC) , то задача Коши
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGUAAAALCAYAAABmgkPlAAAACXBIWXMAAA7SAAAORgFJERVUAAAHZ0lEQVR4nO2XeVDU5xnHPwKyy4LLCiw3IiwCLhiEVWFXwiGgeCRapDpR23ikY1sSNKamSeyhSbWZaIq10dHgMVqnxqoxpkEdDyBUUTEGdeXwBMThMtxd5Fz629/qKmqCTvmjf+Q7szO/932f93ne537Wxmg09tIPNv0xDa/U3zF9lIdlr+FmPr/cfIx/rl3Z3/X/CT1t9aQvWcFbGZ/g72AzIDzzd6RxTPkmK6cFDAi/x5G19fdc95nL0knBz0S/YeU8VDMzmDpKKa6fqmXmewtx/un7zAi2Yt3az1j027/iLOtL6qTSseeDULaseYcXFqxE6yF9rocb71Wxd9NGDlQ6s/Mvy7C3epLG5PhtR2vYmLn5uXj3B92CjYy5c5Z3/pzN28sX42TTb1xaUFWUz+HcQjqEb9+AcOKTdJa39/YY2PbhBnSvvccUFyN529ext6Selqp7vJmxhghXmUhnCrQDf/8bFxs0rHn3JdJX7ubWmf2s2u5AaOJkbAw1xeRdqWGcLobGklwqmgbRrowmNsidmvObqfHUiQ4xCbx8Jp9Oj3CGW1VypV5O/BgVSeFydpy+hTZV/VyGsbLzJOVXS6hff5AO4yCov8XZy7cYrY2lo6wA/V17mq8eQzFynuVO/W09uXlFeEZE0VV3i4ioGByk/WePKQC+OFzMhJciuXm6AMWoKFTeUbgatlPeMA+n+8Z6YNhv885iHBYm6lnaKOfFCJV4ZijPIfPAdVLnzkAhxKBR5tQnmAzFWXwjCeU1Nzs6Wsr49GQpn+zIoOgfH7Fz7yki3pgo0unPn0TKYGptJZa7bgEa6j7/lD+UDsHm6o0yzn2xhya5irhWwTBtUaSljUNha8OF21fxD5xlFtjUSEtbDTtWrSV5ahwRE/zEfd/hQdzNuonBqBYfaFLqs/Vr0Nc/Gn1DSF26xBIpD3D7yglySypZYNVLRVkpF4/vQ9/txavycvLrAgk0VOGpdBRp26sL+CjjIMk/mU7unlW0ylLQxJgdcreskHP6Cjo77bC1vUe3EZyHjbIYs7y0nPpLWawvu0Ns3FiCHMzGcFa4UdvQCo+8S9TTUMG+1cdJnBJPWFyg5az0zHHqery4rj8vrh29R+AzJsRyXnfnBt6qKeJ3j7EaaY8HPd12uKl8sD7ZaKEbHTsLZfcmDl18aAupvRyrDitKvr2ATUT0VLpul/D1tetccfJmSZIaB1uzsjKZnNq674QvVxycvYkIjyZj02E0CTGoXOxFmqaGOiGV/S0RM8jantHxibg2Gh8xvwTl4EF9HNJ09Wu27tEzbGyYeFc9Tkjb5mq2FV3im0AF6dNGk71VSmt7t0h/av9X+Eycy7iR9uzeAiu2TLbIlMoccZG7YiWW2KHinr3jw3LqH64Tsi+LPxUPYXlEiOVefVMtwzq7+rzLpKdWE8q6zFy0U5LwkD1MBZlkEA5DXfD09DTLGKroc1diqxAc02S2g1FC0z3zd1tDi5BV7vwQjF3ttLT/R2A63NxT/EYFs2vXSca/+nqfcjA8LgXDBj2GFDWdlZfJ/ncxamcJR47mkTxJS4BSQaH+BvGxM/sK6HxSqLX1Q+VMqZ25+xDJcxehP5LFgexzTNJpcPEPpuXEfqQxaWLJ1IyN4WDRVRhrHjAMNdc5cugORqWccv1l3CIjRAMPcfMnSvg9DabMLb1UQFGDO5JrBeQc9xD7gF1HFY09Cnz93TGV8MxdF1n69hwx6/LPVBAihy+/yiZxgtYSgH7a6QwpzKOxLZihsg7zm4TYe+Bk96hkXHM/p7otBiepD8HOQtnMyaH2dCUvzk4VBozVGHTLiFJUU1hSTkVJC0U3QwhRedH6XQUKnxEsmpZidorBIEUXP5XxoV59FLJz0jA7MIfsM8WopK2o4ycRMz4IfU0v7vYSblw4QWHPeH6tce1zLyQqnhC+H92CPtGvpKNVD8fXupl6ibcYDFXtoAmfaCk7vmHx+JfuJOdyAJGz5tN7oRTXwJm8EVyI44igpw4Hj8PY1UNzi4QJ89MZMSKLTu9AehvvcHTfYcJnpYsTXfWNa9yVmA3f2nSPwNhEdNoAs55O9hZeUo9xLF44mNOXyjAlgbzHRjToA1jb+zMtcRjZufkkx0Xx7poPyCm4hr8gJ260UugrzQQlCz27rZlubx2vewslr7Edl8oiTv6riNkLf0aYhyM2ez5egXHkZGYkRz9Vqcg5v+HSqeNIfHX3I2YopnZiap4VTVKWpyX2b5nHYK/0Q2ue/sTS4idE85dbVlPnqCEldbKwa+5H1jJnZvx8saDkWaxCE0iacj8bAjyfWZa1VE5UnE7k6RRrrvemqU6ZlMJYlYu4Ntr6s+wXast7zDDr+TiUfuHMEH7fB1O/cBCCtba1C7W7mmkvm/maJq7I+YsZKU6pfXkUnc0hct4cS0bavPLW6n4VC4tOemLPND0lJDy7cX4Ipj708uIV91e9T5wlJCQMiJwHMI3zTo+svdQvDCj/AM2TgWoKsJFq56fSmyrLoxiYf2M/YkDxo1P+D/FfpBWjhlE5LnsAAAAASUVORK5CYII=) (3.4)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAALCAYAAACH6Va0AAAACXBIWXMAAA7EAAAORgGcnvTSAAACf0lEQVR4nMWTXUiTURjHf5svLj9mulU2pzM0IVOnoFCaoPZhhqKRphYswjS07ordSFFdFJUIdSGEBkKBIhVaMCgi1EKlRKkGJtn0Jkyz5qzlnNrWfJfSaEaDoB8cOM855/n/3+c85xUcDocTL1gGW9E/CaJJX+ixXlVdwoW6FiLk/t7SfELwtmhsqcMYf8xlrGD0aTsX73Wx+P4LR65dp+nGXQzNdfRryyhK1fy1kXPOQnP9VQbMX7HKkgjNzUOwfhji2fA0WZlpjHR38U0RRdvzCc6XK5E4Z2l/YOBQzRXip9o51XCfXZd17EiOpH7A6JP5xJtO+uY0NF4s50yFjpsFjQjDpjE6W1qRRdUTYB7B5BeOM0hKmNTVDYkF6ycpKqUCeUgM8s+DolDI+mg+To1iQ0IA7q6Nv3pEQ1u3h+GWPaXoclLE+Yx5nAhFDFKZDK1KYN/sIEJaZj4WYz9jIyYi16ZQnKqmq2NeFA50JS047FhnbSxap5kLDBaFrFbLb5XJN26mIFeC7bufGNula1BrVB5npmam3bcw42SICHfP41Ni6XjYw/bKKoLkMvI2hDAwuUBmuIpkrQKDoYNoywAZhTVi8qjJRGJS+krVyywbLyFzzHnsqeO24Whtov2xnBckYD9Z4Ta3LwSTvTuPhKhQUa6ouozGO7eIPHCQ/OO1rOvtwRagIycrjol3ffSOKCmu1HpWHh7LTtdYDbkmjbOn5+l/a6b2nJ6YqDCE23W14Hq5JXuXxNyV+CsTOVok5fWkmU1J0eTk7f8p4eSl69UfPlFKqMzrj/JH1PEZrrEcORF0+ksrwa8Eq7aS4dkykfTsXJ9NV8P3z/+H/FfzH3jy0+vPkTbOAAAAAElFTkSuQmCC) , (3.5)
имеет бесконечное множество вещественных собственных значений
![](data:image/png;base64,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) (3.6)
и соответствующих им собственных функций
![](data:image/png;base64,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) (3.7)
которые образуют ортонормированный базис пространства ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABsAAAALCAYAAACOAvbOAAAACXBIWXMAAA8BAAAORgF7zHBhAAACjElEQVR4nL2SW0jTUQDGf3P/1jZNlqaWzkRXecu0tFy6vHQDRcJLWi40QYREX4SeKnwQSQq6kIVdKMXESIdERCGEJVhJoahRWCBqpaLmnDrmmrqlE8Sk7CX6Hg7n8J3v+51zOILVarXxnyQsDA0XtdxqU3GvshQvuY2RnlZuXNPheSiTrF1zXK3rJPukFon+PSVX7mMZGSc0/xwF8UGrls8YvlJ9ux6v1GzUvm6LMBf3EJK0CXbQgswmC8HqaKKiA2goLyMm9yzK9TJ0FXcJSismz+8zWcXVJEdeWMosaGLgA41NnSjD1POLLwSGR3NUG8v5qhp0IbmLsPd9vYRqfO2BOeMAdVW19MtU7I7bR/OYnmQPKSLROMN9RrYe90LiPYOPZYwp8xzIHew50+Bbyi7rOJySTkt9CYa1yQTtlSB3cmdi6BsPXtUjiAxd9I/7keqpwDx/bfM6b05fumkvmDWOIpcKvzyN3jAJkwb0IjlrllltT5/jEZVBbNgmHlbYKCo/gkJsY1aQIjhImJ4yIvS1v6ZXIqO//QWVdS/JLC1G4eywVOI8J2HYZMPRUUpEfAg1DXeQ+ZhQaBKR61u4Xmuk8FQiDmIB02gPz3RdWDc4MvixDaU6AvGPSSas07jtDEaYdQkiK1rPyHcDoceOoloGEpzcyDkYQNO7T6gOBLInowiaGxmyuHImVs3w6zrMgpd9b3iKluk3Hbhu0VC4zROZKhgnQUR3Rys74lLJiYlBUIXFoAr784/yO3SCoUf3qHw8QXpiJJH7k5e8qY2h5Eb52+dShZKDCcpFY+viAVqf3KF7yp/8dM082IawsnylRGIZmrQCNL/xNgdvXzWrTspDvWz9V9i/1H+F/QSfMtfzu8zLDgAAAABJRU5ErkJggg==) и не полны в пространстве ![](data:image/png;base64,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) .
(б) Если ![](data:image/png;base64,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) , то собственные функции краевой задачи (3.4)-(3.5) образуют базис Рисса пространства ![](data:image/png;base64,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) .
(в) Если ![](data:image/png;base64,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) , то собственные функции краевой задачи (3.4)-(3.5) образуют ортонормированный базис пространства ![](data:image/png;base64,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) .
(г) Если ![](data:image/png;base64,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) , то задача Коши (3.4)-(3.5) вольтеррова, т.е. не имеет собственных значений.
Достарыңызбен бөлісу: |