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Chandra, Harish
- Effect of Frost on Jatropha Curcas Plantations
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Indian Forester, Vol 135, No 2 (2009), Pagination: 287-289Abstract
No abstract
- Julodls Sp. (Coleoptera: Buprestidae) a New Record on Israeli Babool (Acacla totalis) from North-west Part of Rajasthan
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Indian Forester, Vol 113, No 6 (1987), Pagination: 454-455Abstract
No abstract- Roosting Behaviour of Rosy Pastor Sturnus roseus L. Passeriformes : Sturnidae
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Indian Forester, Vol 112, No 4 (1986), Pagination: 371-373Abstract
No Abstract- Belenois aurota, Fabricius (Lepidoptera: Pieridae) a Serious Pest of Kair (Capparis decidua) Plant
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Indian Forester, Vol 111, No 7 (1985), Pagination: 563-564Abstract
no abstract- Local Spectral Properties of a Composition Operator on LP Spaces
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Affiliations
1 Department of Mathematics, Banaras Hindu University Varanasi, 221005, IN
2 Department of Mathematics and DST-CIMS, Banaras Hindu University, Varanasi, 221005, IN
1 Department of Mathematics, Banaras Hindu University Varanasi, 221005, IN
2 Department of Mathematics and DST-CIMS, Banaras Hindu University, Varanasi, 221005, IN
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The Journal of the Indian Mathematical Society, Vol 82, No 3-4 (2015), Pagination: 219-226Abstract
In this paper, we discuss the decomposability and single valued extension property of composition operators Cφ on Lp(X)(1 ≤ p < ∞) spaces. We give a sufficient condition for non-decomposability of Cφ in terms of Radon-Nikodym derivative. Further, we prove that if φ is conservative or it is invertible with non-singular inverse, then Cφ has single valued extension property.Keywords
Composition Operator, Conservative, Decomposability, Decomposition Property (δ), Single Valued Extension Property.- Hypercyclicity, Supercyclicity and Cyclicity of Composition Operators on Lp Spaces
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1 Department of Mathematics, Institute of Science Banaras Hindu University, Varanasi -221005, IN
1 Department of Mathematics, Institute of Science Banaras Hindu University, Varanasi -221005, IN
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The Journal of the Indian Mathematical Society, Vol 86, No 1-2 (2019), Pagination: 187-198Abstract
In this paper, we discuss hypercyclicity, supercyclicity and cyclicity of composition operators on lp(1 ≤ p < ∞). We prove that no composition operator is hypercyclic on lp. Further, we also prove that CΦ : lp → lp is supercyclic if and only if Φ is injective and Φn has no fixed point in N, for any n ∈ N. We also give a sufficient condition and some necessary conditions for cyclicity of composition operator.Keywords
Hypercyclicity, Supercyclicity, Cyclicity, Composition Operator on lp.References
- Ansari, I. S., Hypercyclic and Cyclic Vectors, J. Funct. Anal., 128 (1995), 374-383.
- Ansari, I. S., Bourdon, S. P., Some properties of cyclic operators, Acta Sci. Math.(Szeged), 63 (1997), 195-207.
- Bayart, F., Matheron, E., Dynamics of Linear Operators, Cambridge University Press, 2009.
- Birkhoff, D. G., Demonstration dun theoreme sur les fonctions entieres, C. R. Acad. Sci. Paris, 189 (1929), 473-475.
- Bourdon, S. P, Invariant manifold of hypercyclic vectors, Proc. Amer. Math. Soc., 118 (1993), 845-847.
- Grosse-Erdmann, G. K., Manguillot, P. A., Linear Chaos, Springer-Verlag London Limited, 2011.
- MacLane, R. G., Sequences of derivatives and normal families , J. Analyse Math., 2 (1952/53), 72-87.
- Rolewicz, S., On orbits of element, Studia Math., 32 (1969), 17-22.
- Shapiro, H. J., Composition operators and classical function theory, Springer-Verlag, 1993.
- Singh, K. R., Manhas, S. J., Composition Operators on Function Spaces, North-Holland, NewYork, 1993.
- Singh, L., A study of composition operators on l2, Thesis, Banaras Hindu University, Varanasi, 1987.
- R. G. Rastogi (1929–2018)
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Affiliations
1 Physical Research Laboratory, Ahmedabad 380 009, IN
1 Physical Research Laboratory, Ahmedabad 380 009, IN
Source
Current Science, Vol 116, No 5 (2019), Pagination: 845-846Abstract
Professor Ram Gopal Rastogi was born in Allahabad on 26 December 1929. He obtained M Sc degree in physics from Allahabad University in 1949 and started his academic career as a lecturer at Sagar University, Sagar, Madhya Pradesh. He was keen to do research in the field of ionosphere and on learning that K. R. Ramanathan was starting ionospheric research at the Physical Research Laboratory (PRL), Ahmedabad, he joined PRL in July 1951 as a research scholar. Rastogi was the first student of Ramanathan to do research on the ionosphere and in fact the first person at PRL to do regular work in that field.Full Text