YOYILMA HAQIDAGI TЕORЕMA
Ushbu paragrafda avvalo Parsеvalning umumlashgan tеngligi dеb ataluvchi ayniyatni kеltirib chiqaramiz, so‘ngra bu tеnglikdan foydalanib, yoyilma haqidagi tеorеmani isbotlaymiz.
Kvadrati bilan jamlanuvchi f (x), g(x) ∈ L2(0, ∞) haqiqiy funksiyalar bеrilgan bo‘lib,
bo‘lsin. U holda f (x) + g(x) va f (x) − g(x) funksiyalarning ϕ(x, λ) bo‘yicha Furе almashtirishlari mos ravishda F (λ) + G(λ) va F (λ) − G(λ) bo‘ladi. Parsеval tеngligiga ko‘ra
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVYAAAA4CAIAAAApREdKAAAACXBIWXMAAA7EAAAOxQGMMD9aAAAdiklEQVR4nO2dZVgUXxfAd3aX3aVbSenubkTBBgREBDFQsBFRLMAWAwwwMEBFVMpuxaIblK4/ioHSDRK7O/PSLL3CrqLv/B4+MLN37pxb5557bgwagiAE5SF8f3Ph3JPsb6V48SU7XSykGIglb/xupLYyMtGyyC600edBU+GlMBThZ/4dH/+oopIqnNZat40z+TA/c+9delCEZGai5daytlBkBv60hDCUhCpNEfz+4nmj6aEzTujaJK/FZgsLT6wDcrDW23cLYhBg5euQ1z9s5vEgqfFmmImCz3wYPWXdifPsxJInWxfOsdvkZVTySWyT6yJ2JKK98N79RDFrLfo/LSQMBaGKCsAXIATndDR3BIJVY9edS6U6JidtE2O7biCQnJpsbSkEBA+GGm+GmSBgZSmz6syO5o5A8pn43K+10rJ74pV5j71LYWNE5BgKvxIRUqg/LSYM5aCKCkBPQzQWtCKUcAgE1JCXSbt0p9BN640y4ZfMeNFQTUoZURCuQ5MUJDtLa2opUXlaRwkRyzI+S21elbB/8WGRZ/u0mAHCt4wq7CzYfPu3oIoKQInOEHsQ4BtPaGusbeUz3bNHEWOr5LFrlcltQTEubo1Vu2bCKmCyglXTZbt18UIjsbm+Bim/6oCrQMu8QLc9lgs5xIQ5BGc7ubDAroB/Cyq55RjkzDfIkd4QMjl024Q674KhKMipuiscdUlu0CjanX9q96fEgaE2sGceBub/GlgFwMD8X/NbVADUmODt/phWnq2ByWyblRjN73gnDGUAfzzadzxbUBL4Ke6w2WgK7Aj45/gdKuBn9J7NSdqP7d8pG6e0Lli0VxZ2Bv4tQGVBm4+2br2L8BDbRcO/wmg5y5+WCIbSUF8FQBX3fR5MW7yfe6ZRZEojrwzc/v8eCDlXzmZpeavzq1xJ1UKJsfxpeWCoANVVAFTxNDhS3NSXFUADkgoc1H4dDAUhZIfdLtE5roJB0PLJyvxpaWCoA7VVAFTz+nECj4YHPIj8+yAWPnv+SX69Cu5PCwJDTaitAn7GhceiVOyl4JmHvw7w+9tXeULT1dlh7f1PQ+Wmic+IjP+psAPuSP5CGuMj0xnUdknA2vvfhrrlSyyOjf3OZ6AEDwNGBmpMD/OPrKUj/pdaorr9+FJJ7J+WqJu21MiENtm9ipNEnL8PqDLmWmA6gb4hM63N+OCBebyTdHMFVVUAVBMXmY2U2gJ3JCNDLAh5hV2xYwMH0BK5WXmtr1rENrHJMGlCyI+Kq+aaKcsJa+/x0RYblCy+0UWPDqoOtlTbejs5zJpjUuYlVRtnS1JkMkFkoywDNV/yl4MvjL0YwuxgtoQNKyDMUZT9kYiYDCoALIuNLgSkt8FOnHECVee89MtT3KxngGESEqQpzP1ORHBMysykplCErKj4OpyyguiIL4Hqnuxe+7CFX3nJvo06ZJ1GQ6zIKwIkJDhHNqoIJbkfGaUkftfZNoSyvI80khKj+Mzw3/I+s0iKMfaGIH6873H+XVGdqIu/syIat8A3VQ/LBnTYjfGxpdqLlCbH2snmhKj3RIENsmPtCwS/h2zbHgnxaqw8slr518YMTUW51dOkBUY5NwIszy9Ei0uy/wkLGl+aV4yTFGcdOf1Q08f8Gj6paX2pbv8Q4HY98Tuk7+ljOw3JYx8a38KI6RoNJwK6HiO3ArIAq/IKQQnJKaPkRduX3BIOaZFfPdCFiioALE1O/gKIr5YZxReIr26RWHf6sPoQMVrzAo/dbeNoSGoy8XHVZ+y+SSy5fzAAt9FdarTXormw7w+eLnfZpk/9ba2EL3cO3GRychtVIBouVOLBM5U7tmh3qyWUiMV+71khTocbuo5sQzGys3auw33gfmOKd6D11CFCQzUJ/nt27gtk9vz6ZOVvcs/jsxLSfmLlFcTHrB+tlaDqVm8XyT7LBfzy0ufCpcveTwmztqzQYu08d6CltjQv4t5LevfcKGfBrjoMNSSeOZptdNCh96m2jw93bw2YuvvmLm2mviQiORkLPY4Vr3OdN5WSWgBqKnzm5/e8GGDnZMYg0Vg2GfMVCulH7vEe2qrdrYAJn0L2h01x2d1brsTv7w45n2xZfd1zXr9bC2CY2hhwKMBo3yqpbi2AUVp1Ul7He+uz1q6CpWFh74itPd/PLcIoIMxgaMsEv4Wf3LXLI0Lt7mf/2aOqT/DH44OXEev298oDViac3nLok8Xlc5bT+k1G7FQw8vCFOreNKr+kBaioAlrTEjOJTKby4zgfBPx0eZMf5mww19XYEmxv6RM/XvFIm3niCNcY1QEtYu3It9XjqcwJE+o2GELh5aPZ804fHE0zd0Ijbrsx2flIuJTn3BE6lZYM34Nx8/zOmgyXNoBNy85S7th7Ac3ftlUf/JGa+g0humI8QzikwFzntTl3zpWae3vtFO8r+yYTR9fWHuMNqnvtcYN583nZ/nqPFVm4c+Flme3+ljEuon0PIXlNnJR37w2RP2NLIWcaWBXjabfllfjeq6e3CeN6br0+sHD6Va7TBT0GGD73/PGihT42/bUHxTvTZVmAxLZTlkae6v1mGoP6etu4zafTfFxHmPKCaiOOn6pyvHFAi3GYokPyz15jfOlUk77K6CdogZ+vH07QPX60/6w9JKeW41pR6RVH3s2/PIuuLyBO1m5NotOxKHGP6Yxk5EUP1FMBhNyk940oaWWZXz8hDCx9+eSjzC4xgVneN3rvQXVPvd7K7lpDTtqAqeZLsUtOJ885ojHqy8HPD8JKZtvojussPKjmoWeM8v4N5DyM5LFcAiz1+WB4UHmonU/88cL3teh+r3k8iMKQoBpLW83BYYgFsUlY3eXCv81H0JKWkElgmC8vOq43QrXxUTk8uqeESJ/G8amp4rtLg5Dle4lgdYt/YKMGuBba6u/0uV3o7EZyMBnAMtuO38rzndlZo1EzGqp4GZaptsRoVKUPVb3eariuZOubcDvh/oqB5Ji5eDp3poBe9wugyrteyRpHnOgGPss0a5mx46bgpEPquiQdNo3UylnejoFfbq0TGKqi2vLDLhXM8tqjxdoee+shj82SIQXYnhqZJjHz9CijjQ4aXno9F3MOGzSyxWkvtaBdFBxxatYCEj2NErQxb1xxMVd3pzTZRUc1FQBVpCZ/AjkM5MZxTmhrWkKu7Ewl0uYLld+7Xjn7khCZkWGULeXdL71r1pg7WsUBK94nFOla69KPo3cFv98ObJh3nZ9MgXAalpL7rkW1KBvRDvwBn+FlYXu0EDh2DMI3t2qeLbYe8ixUERdTruWs+Nu8BIScpPdNKEkl2fFNCLalRCZjtBwUuuTF56cXCirK4JDsahqMXbWtLe5apLjNTrrBjwHsC2yNtnmEZu88qEBSLVESlrof3Z/UGFqzjVJMYE1OfK6Y1WgqACwNWb/8nozv+5XCgzoGJDvv3HkzuqMHv4bdajMOGmp00E1fakpcFRx7TNeQpAgBtnkmWJNbuQ7ugza/QfVvt5utCazEnHQH25pRi+6WLBsiESEvOplVf/2odQiqfHjtu+GZocoYo7bUkm1+8Ov6BebMJLfp9S34jgQkOZ/QJrfrpZoKaP2QmIGnUVKS/rWKC1UlBQXeuPwSw8wb4BOgZbNSt9s2ro94Va28l3RWBf816m5kKdCWEdcwx1a0+GPdjzev6Z2uOXdrDrSUjkj68/f4uXoTbzhgZfTFi4kYoakN+elpUZ8Nwu6t5QVq371qVD1Gapq3f4m8G12GbEmP+znfVvDjx7qS1+9YXa45ynXlMVpWRzA1PANvNKiPp1FwTaxxHeatP3OCzjxs4BNnhwh5L3NVFmnhxk41ZQDLU5OLQVZduWnjMgII2VHxTarbNTvbOFT9+lkK3xbFztNIpSW7f854kcSrfXSYYgFY59rOddodmr5HQZXkZyS/lkyxX3yLtfEQrfErtMV57nkyZXXSwqGLVADu5btXY7qdFJVvwlvVzjANEwFOx9YCYxUSddJwLqkgtBratGfffHOVFRzQkgFmw3P5jeeGRgPVJFz2jUaJiNATG9Oi6rT2yfS3QbA65caVyHYu9vqsXHY7j9WyOERTdHipwvbhfCFoeRtrnhlBL2vMlpAqR4ySLrf76zyCtgKZbZtaKoBQmPy+DuCTl/vF4TjAoWFrlxdysn7Nvh0L+3OaUJheyKcu0l8l27PDwhHGDtYs+CnRkhtvB6R6SYbExCP7HAcIjKgEXU5GGahHbj89AlBtuLOFv0JgqL0wmpCarxg2bUPn2L+jc/s0zYDEzdGWHvoabWZvzYRnfSu26WFwsofYjcgkOkxf8jFi4mjfzGpIk4uMHGnP9LZwKnN/fFyPCVEVsGCT0GyfTm0zZqq7AT8/Pnb2XQVx+C9EADjFlQdWKdEO+2PXyz8kZRLQckoy49KeYElc7Gc25qKgMydqC96Ehgv65pFWMqg2KwclaTe8fcFoaDWnZmtwykFV0j4MLSY1JTe9mGg8kV2m7fGhd79LrV0sN1yNBzCYnrQS8tO/Cc7nG7bOYNQWm9KZB71pnGtKMhwF2MSFKwKy8AhBMmwmqD5yl9lJnov3nWUwxJwjp3LUdqn1PdaYeNju7LQzgWuFaQhp7lo7Amc9W8ddlJ7PIy02bDNFSy2yFDgd9LTKagXp6g06MdHWkKxmhALzcA8NEw15wX6ZpuyMIiLGSFHy11+Az07LF1NVGOBgIVaUtzGz9NcAqAmptECvo1WApdm5RD13TTo01v7SZZInkKxsTJX55SBiYirgZ5zHtnBVv5PCneloLytt1VjYNW0HVpS3s7D0Rw01YlSMO53Z4LfsPPR0DzVaNGad/0VSgVjYmSu+lhMRXGNmCfGj39ZTDOsydTud44TvxaXCBtM7a+XYqe55laCp+2nT8SaZ+CkzuwHgkpMby+86PA3xkZncFs8ObdWlQYCW/N5pagOaBlhZVsXIyTJc1FBtfEAivSr+YXD8UW2D/vIH6FmZalM6cm4CKgCqKSyoYlBU7fdPIsCy6CtXXqZnfyisY5bUt9myc2FHS8OXVxBYhne7/swKegYqsIcHh9eZWJIEQbKyYytK6yDE0MmcwbSmeDo/UPDJ7vKP4b8VVyrN1OnVJsScs84vNK/FCndWL6i1pbYg9zMRMbWirIVZZ1gTr+2/u3fqJERigx+VLXfgHiAPU+WPjuxiJi+7qKQCOjrJnDaUiLzscJ7Q0QFL0zMhOYtBLgQ8HsD296gdqle6a/MqVB8XWaRpozGMAsbisEQCYVBH2Jzivy8wvbXnLlieHFf73TGlp0MEUFyzXdxNSR07rdEBwa3zbqt1lQE+MypVbPrxLu8CsR2PxJKUDMDRI1BNbORnTXvVoYUG4Gg7BSIjB4i5QVfSVLbf6fISgT+iY2q13KXR5KWaArTkfCgk0OgoSo+rbrSlRCWhNVf0OC5oNedMH2hUQ+1teAx2qORQTcyxXW80jp9Wa3+7ODjay2B2vw2IxNGih+Rce/bNvZcSm3qKEqpNj/32wbGgx2kGIJl1HQ9ZkyxLRaJQAAMTA0nZIrn01+7RinUWn9t0INR1Yfcgk9COpyGtaL00p/u63OTac/woc4J20POaRUtJrFscLa67po1V19tirgRWG93Q7Eo9ITMiYeqMrb16Fp987SZo+qBbYqgyK6OMx4Qf1ZFdnRV/aFStBYE7ziOcTp7gzpQLeVCyemN/Twd0ytNMHEOWfqijAqDa7MyvIJ2Z0vAWzKi0Zab9J2kgN9AIBRgZwbp6cGjgpHcporo+nT5RsKygCCcu3queoYb6RgYWpkG9Db3amlNqfVeE5L3bcp3O2I24CBaq+/K1RX61QlcZgF/jkuh1V3UHRjMzEWvrhlraLQlv0yT1LneqCfBHfhGDhHjvNDdYX9shEDkqkfituFRMQ6WrNkP1sRGF6jbq6O/5hUwS4t2Pj5zqngiKH3h4vx1xIECrvOqwvcpIA4GOMVdOC0pAQX50P/VIT+dFx9UrO2l2e2GRXHKygwIgmVgYGmo6co40eqg6aq/9VZGTVw3ZaQg2i1mMg981zTbu83QT6usBpsE5h5Fd7nl+ee8VMf/U1ldmPk4iI1guALu2gUxdRH4VpE/SYXY89i6yTHKJep8wWGbG1tq6QRWt6b2P/XGi6/VFfBjQ0kb6WNDjCptVfX0+1FGw9LyMY5tMUMPXr43y1kpdGgD8HB2L1/EUIxblfRGUEgYK3kRCuue6vX5Qxcsn/81cYzkNiSAydVT8wfK05l9d4/pl/fWDYlgE81IdV/97n9c7C/cKANbXNdAzk9/3UkcF4HM/5BJoFLRUft2BQyz6kMOh5DzIFkMLiXNVlzdAiO4GSMi9tsGb6HLR5sfzGJSUTYcmherjX6az2Ur0PQFWlNULSPBPbB4NYBEW4aLDdZlmNZFnr//Q8O1xzaKERDmqK5o7amLXZXuW3wZfmt3nLYtfxNNJO3RICdVGh2fxLJfsF6iytFFAhY8MgVDC4iKMdLSdKW0rCAqME5jlhSuITG40B6+tGSPVPREIme8/az6+JEMN2RnFIIO55riMALA0NuaTuJH2yPvCkNyiAs1xFSCib3IHqopwXexBc+SBnWhnRqPlrZdwGQa/qje26BnMdowdagTEhSdWVVFS6z1Xh67fEjw72FawJ6r24seBryo41EicTGghUdaqitbecu0c4aWdsnb+uPGur2JnZUZOW2Srcijk4Y+V63onDQgVFVgR4ZFdK30AzCKiPAz0OKAzl1OuheTIuMgTEh5k8AtLgT+i3hVONeftlANqiDkZhNvvt6zLIyEkzlddXgMheHpztCXXb5lDzOLQ693LaTmNbQ22n75btLlvDQZYUdouNKdnCUZL/oOrKby2y9RHVujU+aZgWVZ2OYLfSmMc6zkaMz+Uya0cvLEIOU1LtTogrc1+btcQEWpvaIXas56Hs6zwcw6NvBVSCoDTjKxIZh+gmtQ0Ru2VE/36Hc5wj1fMqdOBCDlcXURmvZpjr+cdJaStUhb2vm2FYZdOh9oa2kAg4/lrltX+G0Ijg0K+gpDgHCuSxXVQZUoGm+5GcnZNoyTWe80/cuvWfRkcgVlvp1Pq01fBqaIGtjR1CWOkmgIQ8tJz29GK2qpk1OkBQJVx1y6E3buZ0A7SBRw9PX3JZlPx4STDqelw+qaUgho9pmvzy317SzeEXOtbFYiSWrFZ2/D6nRIzh2633M+0VILWronusQFYDU/HPgw7st9+q4AELycrPZKI4NTc4buDsYBkUTZKTFup5Ek63ka/+x4+xdMlxtj/9oJenzySx3KzubfXzTyH3d2uCUJ+8kcpXTlyCgGjv9sr4tzFULQwAE1Z7L7q7Pv7YSgxU30kVBf9Nld/vnPK3YcZqJqCr/pXQ0y6Xc1IHi21Rt+0lg083b0pMe+8yz2N8w+se2drALYFjsuPbruW6ny8exEMWJKSy6/r3l1PwdJof88DNFiDB2tG9IlR55uCOR9yiQwztcjKl8GPphVrztcdYj3QqFjNOHb3Q/tcrc600Sg637zS88ss1elDo4Hqo+MwZvsmOBuA6JzLMj3k3elZa4sI3yNloN1nnGI0rPROPs/EG6p1JhKruv2Was8vRqozhhGoJiqe3uIIN1kCAay620/2fc1j5nXD3n/HSDUFgKqyM78DQovVyZOUBIBTx35/x9/ZscJxmSxi2R5Vs2lZd6Omn3chdt6AEEh+u/uFdn2XPxMjGueup8R3DAFGGevjgYMWXqjuVyC9xOpYaZ2JzCHoK3Y1DRp1j8hHAyNhM/HP6/8qDvglIlvc0oW8ZZQdtemgZ9+VToBFz38tSW9TpOf6mHSa/oNAK1jNrr6R0moyvav3QEnteBE+MASDwamM931XUEVECqfFmR5XBVJ47fNi1QfPRvMMUEMFEL9kZdeh5LXVfmUY0BjhZu4ndHFP7WftNQeG0fgYlfUWFz2f1WqakzFGBYuDHjE4nBuaoQMB2GWUBGhHjA4seXkioMnSzVIEBZY+9E/R3XCAZEIPq7nRxM87vF7NmIzJF+J/N5+yr704/GTTZKJrCMc4Q0uGagtGEAC31UbeDTcKbLZJktGsobJ7oW1Lj4y12A1gFlUUZpqgodAFTnfTvKu+bxsV55CzELU14WqymqPjcOsIyAef8Taey8hleJuZRn7NkobDj6v0rcixgwjZAW8EN14l8W4RPn6BhORGqXjUKOm23PRCaJqDxi+tC0TSsAgLtr+6j3M8PGfYDEXyL3NTdfOLnblTb4xdgGDJfb9SK/eNY24WRIlYrxIZ+WdieVZSThPPU0xGdU5K+eJbF8wG+A2Rgnau8m7+CdNdhl0BThrRlztXape5zfyFhdt/CPBHdk4VahzDgF+CQX/3yhiv21+O2AiM0bKhyvALWUZ7jo8534bkXrjamDLSoUTsd0u4+SfrbFMfq29vzbx6l8PliPzEhmJQVVbx1EV7xEfICySPtbuOq1/kLNcZY/V++P9uXgfX7tPqLz3wW1QOl775aAJSQQUQP2XlNtOrasmSkTE07LT5F5y2JNkcctTb6ac7emC06Mrd04MfJVQu1x7lIAtC8YtnwEp344mfVESjsuN+aPe/phbDBpBYvavq1qNkcVuN0TYLFz17ibN3ndurxIlFd/afefupQXLn5DtBAp+XkQ8J26uTvyQAxwkkn3By1lzluUaV7ElKgM1oh/3jG8+LVpqIjrZZ+Pu7R7Vme6zHsuYoDUZ6zc7qm49SxJaqjbZZuDH9YbL49i2qvcZu+/srO68mliJnLPrF5XDca+5GjhYAJWTrNivkYWz5Cr3Rtky25j95x7lphwFp14fkN7TgH/31VFABP3MzipAKq8kZBgAsJp53fuFrowCbpu2KMcKghRasEyI/yokBcOgsH7r2eyA0oqbrREmuUaKLPc4tpqZU44b4NTunnlH1F4YBSF6bM2E243gVVsx0jdiYkRs6jCfuiYOcorfSdowwAKOitQPpDYyyg4+yw0jBJwTAorbUbqxAOEmLdZJjBRoK5VUAoTA9Fy9kqjWO7UEwf5i2nPQCpPJqdaoOA2AmFxRXAVDNh7RiVl2DYddiw0xqCPkpH1pllunBp73+P0HxhtqenpRBo7WSSotXYagIVPM+9TO3nv5kOLsQ5rdBaRVA/JT2oVl1tf7vOroPhnJ0aO9MJgOnYU41gfmHobAKgGoSYz+pLzaFHQF/H4T8uGTU/GMGE9qVD/PXQVkVANVFvPigtsR/sn41AWZkiJ/CX9XNPTDMMZcw/zSUUAFg8Z3tBzJneR2aCz0Oypi5/iI3PAr4W2hJ83W6CK49u1mxKPROi+0F2Ab4v4MiKqAuKyb1hx6h+tXRa7T7bprC36H8eyD8SInJFlqFLw48+Ha69yPyV/fA/CtQQgWglfY8CYpOjHpSYxN8U5cX9if/RTAan3/BEZP2KJJj36MTCr/tlHKYyQNlfAEYLkUjM0WKRAXzewEYhLTmCWn9aTFg/hiUcwcSPj04fadaQAj97Suj+ZZFIvDUEgzMXwClVAD445bbfe7zN5ZwIKpu2G4O1QteDq8xg4GZ/FBKBTRFP8vmdO5aEMQswpV7Lqp5+WL4g8IwMJMeCqkAsKa8EonFdvX7AC0tUFVRByIY4NUBfxNNOaE+12I+ldTQ6ax32zCdh6Yp+/alR8VoFiY6Hh1rM3mKHMgBM+mglBUAkJygDEEQkUj+IcYwk4H2D4/i+Tae9GXDf33oZDrb3tlT/+tn6c2uVqxIRFvenYcpYkvgDYT/JBRSAUjWKez4jz+7Tq2Gmpva2DhYYRNgEgJ+e3U+IK56gH5GYiUWOluzlbNqGHV+mAozzezc/epF2vavzmTad5ciVkya7uV3ImJ8XxmFmdxQygpg0DUSu/tfDaQ/FVFVUCI+Ww92BExGkPyznfbNHu6Xn0wtmeWgfOfSbkJpRon8FtsYN6tjQo9d1ZkAwpesaroFcPv/N6GUCkDyrzqxyNPPL0QMVVxudXLnxM/uhfmt0GlqM924cKGZ0FxXi1a2P+DK3zznquveReacYoKcwvOct03+gw9hxgXl1gVgJZbu20ux2GB+N0hufTtHfZIbzMoOF55R5xwsmEkEfLYPDMz/NbAKgIH5v+Z/eshnlZ9MYIIAAAAASUVORK5CYII=)
Do'stlaringiz bilan baham: |