فضاء الطاقة لمؤثر هرميت في R^n وفضاءات سوبوليڤ موافقة
Abstract
ندرس في هذا البحث فضاء الطاقة الموافق لمؤثر هرميت التفاضلي , ونبين أنه فضاء هيلبرت مع جداء داخلي مناسب، وهو فضاء جزئي من الفضاء .
ثم ندرس قوى هذا المؤثر , حيث نشكل بالاعتماد على النظرية الطيفية , ونبين أن المؤثر له خواص مشابهة للمؤثر من أجل عدد حقيقي موجب s.
لذلك يمكن تشكيل فضاءات هيلبرت جديدة ,هي بنفس الوقت فضاءات الطاقة لقوى المؤثر , وهي من نمط فضاءات سوبوليڤ. ويمكن التعميم إلى الفضاءات من أجل .
In this paper we study the energy space of the Hermite differential operator
and prove that it is a Hilbert space with a suitable inner product. Then we construct the powers of , denoted by , by using the spectral theory . We will see that has similar properties as for real numbers s > o, therefore we can construct new Hilbert spaces which are the energy spaces of powers of . They are Sobolev spaces.
We can also generalize those spaces to for .
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