Misol.№2
Ushbu Neyman chegaraviy masalasi berilgan bo`lsin
holida (4.2.1)+(4.2.2) chegaraviy masalaning xos qiymatlarini va ortanormallangan xos funksiyasini topamiz.
,
so`ngra Laks teoremasiga ko`ra
(4.2.5) tenglikdan quyidagi
tenglik kelib chiqadi.
Misol.№3
Ushbu davriy chegaraviy masalasi berilgan bo`lsin
holda (4.3.1)+(4.3.2) chegaraviy masalaning xos qiymatlarini va ortanormallangan funksiyasini topamiz.
bu sistemadan quyidagi kelib chiqadi:
![](data:image/png;base64,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) ![](data:image/png;base64,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) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACwAAAAOCAIAAADbgmlrAAAB8UlEQVR4nM2VTYhxURzGJ4lSCvnIx1IRhaW1vULIxppYoMmsbFmwsrC2kFgoG1nYKNkoKx9TUpJCIglR8jHPuNN9DXek1DvzrP7n/O8953ee+9x76afT6eW3Rf9tgE/9b4hOp7PdbnU6HTXE4XCwWCxqtToSiTy502w2k8vli8XitsXj8UqlklAolEgkFBCtViuRSCSTyScJoHK5vFwuKVsCgeB4PF4SfIPQarWDwYDL5T5JAMOlUik5NBgMOP10OvX7/WazORaLcTgcWMXn8ykg1uu10+kMBAKP7ycWiyeTCVHjOTabTRTFYvFyEbvdns/nPR5PJpMBRDAYvF3nCwIvKq4zmUwKheJxiPF4fDv5ehYKGo0G59vtts1m22w2KpXqp3W+IEKhEC7t9Xq4rVAoyGSyqwCTGg6HpNuUTmAFkgAFIBwOB8zQ6/X3IFKpFJvNNhqN0WjU5XKl0+lqtYoAr1ar+XyOrLBYLPLouVzO5/PdceJKgFAqle9nWa1Wcl6j0TQajX8QiAIxeDsLRaVSQYDj8Tj86Ha7yNF+vxeJRBjS6Q99WggbIMIqBOWyW6vV8IC+OXElMsBMJrPf78MhmEG0EPLRaLTb7RgMxiMoP8nr9Waz2XsQZIDdbvdVC295OBx+ZntC9Xr9cvgn/h0f+HjjynC2DWgAAAAASUVORK5CYII=)
so`ngra Laks teoremasidagi ni hisoblaymiz.
bundan quyidagi tenglik kelib chiqadi:
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