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Investigation of Spectral Expansions Connected With Schrodingers Operator

Thesis Info

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Author

Zakaria, Kamran

Program

PhD

Institute

Federal Urdu University of Arts, Science and Technology

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2015

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/13517/1/Kamran_Zakaria_Maths_2015_FUUAST_Karachi_22.06.2016.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726509250

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The results (1)-(2) are proved in the present research work. (1) The estimation for the solution of the Schrödinger operator in a closed domain. (2) Problem of uniform convergence of spectral expansions connected with Schrödinger operator of continuous functions in a closed domain. The summability and spectral expansions of the first boundary value problem for Schrödinger operator in closed domain are discussed. The representations used in this research work allow the methods given in [20] and [28] for the spectral expansion and summability of Schrödinger operator in a closed domain. The new estimation and summability connected with one of the Schrödinger operator in a closed domain are derived.
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حالاتِ عرب

دیکھا، پڑھا، سُنا تھا کسی نے عرب کا حال
جس جا قبیح رسموں کا پھیلا ہُوا تھا جال
سچ کا تو سانس لینا تلک تھا وہاں محال
حق بات کیا ہے کس کو تھا اس بات کا خیال
دختر کشی، عناد و تفاخر کا راج تھا
طاقت نمائی، سود و زنا کا رواج تھا

اُس وقت کب کسی پہ عدالت کے سائے تھے
انصاف و عدل پر بھی علالت کے سائے تھے
جنگ و جدل کے اور ذلالت کے سائے تھے
اور علم پر بھی سارے جہالت کے سائے تھے
درگور زندہ بچیّاں کرتے تھے جبر سے
خوفِ خدا تھا اور نہ ڈرتے تھے قبر سے

آشوب ناک دور تھا ایسا کہ کیا کہیں
انسانیت کو اس طرح روندا کہ کیا کہیں
شیرازۂ حیات بکھیرا کہ کیا کہیں
چشمِ فلک نے اس طرح دیکھا کہ کیا کہیں
حُسنِ عمل کی اور مکمل شعور کی
اُس دور کو اشد تھی ضرورت حضورؐ کی

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