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Register a new userThe Energy Space of Hermite Operator in R^n and Associated Sobolev Spaces
فضاء الطاقة لمؤثر هرميت في R^n و فضاءات سوبوليڤ موافقة
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Added by
Tishreen University ورقة بحثية
Publication date
2014
fields
Mathematics
and research's language is
العربية
Created by
Shamra Editor
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ندرس في هذا البحث فضاء الطاقة الموافق لمؤثر هرميت التفاضلي , و نبين أنه فضاء هيلبرت مع جداء داخلي مناسب، و هو فضاء جزئي من الفضاء . ثم ندرس قوى هذا المؤثر , حيث نشكل بالاعتماد على النظرية الطيفية , و نبين 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 , و هي من نمط فضاءات سوبوليڤ.
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.
References used
NANKDAKUMARAN, A.K. ; RATNAKUMAR,P.K.Schrödinger equation and the oscillatory semigroup for the Hermite operator.2009
SJOGREN, P. ; TORREA,J.L. On the boundary convergence of solutions to the Hermite – Schrödinger equation. Duke Math , J.55, 1987, 699 -715
BONJIOANNI, B.;ROGERS, K.M . Regularity of the Schrödinger equation for the Harmonic oscillator.2008
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