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Cheema, M. S.
- Some Aspects of Professor Hansraj Gupta's Work:
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Authors
Affiliations
1 Department of Mathematics, University of Arizona, Tucson, Arizona, US
1 Department of Mathematics, University of Arizona, Tucson, Arizona, US
Source
The Journal of the Indian Mathematical Society, Vol 57, No 1-4 (1991), Pagination: 17-21Abstract
Professor Hansraj Gupta was an expert in number theoretic computations and combinatorics. As a teacher, he was well known for making his students think. He started research activities while working as a lecturer at the Government College at Hoshiarpur. In those days, there was no incentive to do research and library’s journal subscriptions were nonexistent. He remained active in research right through old age and in spite of poor health and age his dedication to research remained strong. He was influenced most by Ramanujan whose life and mathematical research had everlasting impact on him. He was able to attract Dr. R.P. Bambah to join the mathematics department of the Panjab University at Hoshiarpur. Over the last forty years, their combined efforts and impact have resulted in building one of the top-rated mathematics department at Chandigarh whose algebra and number theory group is well recognized in India and abroad.
- Generalizations of the Kermack-McCrea Identity
Abstract Views :169 |
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exp(A+B)=exp(A/2)exp(B)exp(A/2).
The objective of this paper is to obtain similar formulas for exp (A+B) in case A and B do not commute with [A,B], but do commute with higher order commutators. Exp (A+B) will then be expressed as a palindromic product of exponentials of operators. For example, if A and B commute with [[A, B], A] and [[A, B], B], and if λ=(1-3√4)-1≅-1.7024, then
exp(A+B)=exp(1-λ/4 A)exp(1-λ/2 B)exp(1+λ/4 A)exp(λB)exp(1+λ/4 A)exp(1-λ/2 B)exp(1-λ/4 A).
Authors
J. S. Lomont
1,
M. S. Cheema
1
Affiliations
1 Department of Mathematics, University of Arizona, Tuscon, Arizona-85721, US
1 Department of Mathematics, University of Arizona, Tuscon, Arizona-85721, US
Source
The Journal of the Indian Mathematical Society, Vol 57, No 1-4 (1991), Pagination: 79-93Abstract
An identity for exponentials of operators, which has been of use in quantum mechanics, was proved in 1931 by Kermack and McCrea. Let X be a real or complex Banach space; and let A, B ∈ L(X) be such that A and B commute with [A, B]=AB-BA. Thenexp(A+B)=exp(A/2)exp(B)exp(A/2).
The objective of this paper is to obtain similar formulas for exp (A+B) in case A and B do not commute with [A,B], but do commute with higher order commutators. Exp (A+B) will then be expressed as a palindromic product of exponentials of operators. For example, if A and B commute with [[A, B], A] and [[A, B], B], and if λ=(1-3√4)-1≅-1.7024, then
exp(A+B)=exp(1-λ/4 A)exp(1-λ/2 B)exp(1+λ/4 A)exp(λB)exp(1+λ/4 A)exp(1-λ/2 B)exp(1-λ/4 A).