Department of Mathematics

Indian Institute Of Technology Madras , Chennai
Prof. M Thamban Nair
Visiting Professor @ BITS Pilani, Goa
DESIGNATION

Retired-Professor

CURRENT RESEARCH INTEREST

Applicable Functional Analysis: Spectral Approximation, Operator Equations, Inverse & Ill-Posed Problems

CONTACT

044 - 2257 

mtnair

RESEARCH GROUPS Analysis
PERSONAL HOME PAGE   https://sites.google.com/view/thamban-nair/
CV   https://math.iitm.ac.in/mtnair.pdf

Activities :

Gave Colloquium talk on "Regularization of an inverse problem in parabolic PDE" at the Department of Mathematics, IIT Madras on March 12, 2020

Gave a plenary talk on "Operator theoretic formulation and regularization of some inverse problems in PDE" at the "National Conf. on PDE and Applications" at Periyar University, Salem, 5-6 March 2020

Delivered a series of lectures on "Functional Analysis" in the "Advanced Workshop on PDE & Applications" at Central University of Kerala, during, 16-20 December 2019.

Gave a talk on "Convergence of Sequences and Series" in the INSPIRE Camp at SSN College of Engineering on 12th January, 2020, 9:00-10:30 AM

Gave a special seminar talk "Backward Heat Conduction Problem: An ill-posed problem" at SRM University Ramnagar, on 29th January, 2020, 3:00-4:00 PM

Participated and gave a talk on "Ill-Posed Operator Equations and an Inverse Problems in PDE" in the "Diamond Jubilee Symposium" at IIT Bombay, January 4-6, 2019.

Gave 4 lectures on January 2-3, 2019 on "Orthogonality and Spectral Theorem in Finite Dimensional Inner Product Spaces" at a Workshop on "Linear Algebra and Multivariable Calculus" at VNIT Nagpur.

"Hemachandra sequence and Madhava series" - INSPIRE talk at SSN College of Engineering, Tamil Nadu, on 29th July 2018

"Importance of iterative methods in non-linear ill-posed problems" - two talks on 12th and 13th of July, 2018 at the Workshop on "Inverse Problems and Applications" at NIT Karnataka, Surathkal.

Teaching :

MA 6011: Topics in Advanced Analysis View View

January-May 2020: This course contains essentially advanced topics in measure and integration, such as Radon-Nikodym theorem, Signed measures, measure on a locally compact Hausdorff space via Riesz representation theorem, and so on. Some assigned problems are available in the link. Notes will be uploaded soon.

MA5450: Functional Analysis View View

This is a core course for second year M.Sc. students of IIT Madras. The main reference text for this course is the book "Functional Analysis: A First Course" by M.Thamban Nair, published by PHI-India, New Delhi, 2002 (Fourth reprint: 2014). Video and Notes of this course are being uploaded in the moodl account of this course.

MA6150: Basic Operator Theory

The course is mainly based on Chapters 8-13 of the book "Functional Analysis: A First Course", Second Edition, PHI-Learning, by M. Thamban Nair.

Recent Books :

Calculus of One Variable

Authors : M.Thamban Nair

Publisher : ANE BOOKS, New Delhi Edition : Second

Year : 2021 ISBN : ISBN-13: 978-9383656950; ISBN-10: 9383656956

Details :

Functional Analysis: A First Course

Authors : M. Thamban Nair

Publisher : PHI Learning (Originally: Prentice-Hall of India) , New Delhi Edition : Second

Year : 2021 ISBN : ISBN-10: 8120317351; ISBN-13: 978-8120317352

Details : https://books.google.co.in/books/about/FUNCTIONAL_ANALYSIS.html?id=p_e2SqpUNNEC&redir_esc=y

Measure and Integration: A First Course

Authors : M Thamban Nair

Publisher : Chapman and Hall/CRC Edition : First

Year : 2019 ISBN : ISBN 9780367348397 - CAT# 322114

Details :

Linear Algebra

Authors : M. Thamban Nair & Arindama Singh

Publisher : Springer Edition :

Year : 2018 ISBN : ISBN 978-981-13-0926-7

Details : https://www.springer.com/us/book/9789811309250

Linear Operator Equations: Approximation and Regularization

Authors : M. Thamban Nair

Publisher : World Scientific, Singapore. Edition :

Year : 2009 ISBN : ISBN-10: 9812835644; ISBN-13: 978-9812835642

Details : https://www.worldscientific.com/worldscibooks/10.1142/7055

Recent Publications :

Conforming and nonconforming finite element methods for biharmonic inverse source problem

Authors : M Thamban Nair and Devika Shylaja

Journal : Inverse Problems

Volume :38 Page: 36pp DOI: https://doi.org/10.1088/1361-6420/ac3ec5

Year: 2022

On truncated spectral regularization for an ill-posed evolution equation

Authors : M THAMBAN NAIR

Journal : Proc. Indian Acad. Sci. (Math. Sci.)

Page: 12 pages DOI: https://doi.org/10.1007/s12044-021-00632-9

Year: 2021

Regularization of ill-posed operator equations: an overview

Authors : M.T. Nair

Journal : The Journal of Analysis

Volume : 29 Page: 519-541.

Year: 2021

On Regularization of a Source Identification Problem in a Parabolic PDE and its Finite Dimensional Analysis

Authors : Subhankar Mondal and M. Thamban Nair

Journal : JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS

Volume :34 Page: 240-257 DOI: doi: 10.4208/jpde.v34.n3.3

Year: 2021

Attachment : View

A truncated spectral regularization method for a source identification problem

Authors : Ajoy Jana, M. Thamban Nair

Journal : J. Anal.

Volume : 28 Page: 279–293 DOI: https://doi.org/10.1007/s41478-018-0080-y

Year: 2020

A NEW REGULARIZATION METHOD FOR A PARAMETER IDENTIFICATION PROBLEM IN A NON-LINEAR PARTIAL DIFFERENTIAL EQUATION

Authors : M. THAMBAN NAIR AND SAMPRITA DAS ROY

Journal : math.arxiv

Volume :23 Feb 2020 Page: 1-41 DOI: arXiv:2002.098481[math.NA]23 Feb 2020

Year: 2020

A linear regularization method for a parameter identification problem in heat equation

Authors : Subhankar Mondal and M. Thamban Nair

Journal : J. Inverse Ill-Posed Probl.

DOI: https://doi.org/10.1515/jiip-2019-0080

Year: 2020

Truncated spectral regularization for an Ill-Posed Non-linear Parabolic Problem

Authors : Ajoy Jana, M Thamban Nair

Journal : Czechoslovak Mathematical Journal

Volume :(To appear) Page: 23 Pages DOI: 10.21136/CMJ.2019.0435-17

Year: 2019

On truncated spectral regularization for an ill-posed evolution equation

Authors : M.T. Nair

Journal : arXiv:1907.11076 [math.AP]

Year: 2019

REGULARIZATION OF LINEAR ILL-POSED PROBLEMS INVOLVING MULTIPLICATION OPERATORS

Authors : PETER MATH´E, M. THAMBAN NAIR, AND BERND HOFMANN

Journal : math.arxiv

Volume :16 Aug 2019 Page: 1-21 DOI: arXiv:1908.05871v1

Year: 2019

Fourier truncation method for the nonhomogeneous time fractional backward heat conduction problem

Authors : J. Kokila & M. T. Nair

Journal : Inverse Problems in Science and Engineering

Volume :ISSN: 1741-5977 (Print) 1741-5985 (Online) Journal Page: 1-25 DOI: 10.1080/17415977.2019.1580707

Year: 2019

Computation of control for linear approxi- mately controllable system using Tikhonov regularization,

Authors : M. Thamban Nair, N. Sukavanam and Ravinder Katta

Journal : Numerical Functional Analysis and Optimization

Volume :39 Page: 308-321 DOI: doi.org/10.1080/01630563.2017.136144

Year: 2018

A linear regularization method for a nonlinear parameter identification problem

Authors : M.T. Nair and S. D. Roy

Journal : J. Inverse and Ill-Posed Problems

Volume :26 Page: 687-701 DOI: doi:10.1515/JIIP-2015-0091

Year: 2017

A Derivativefree iterative method for nonlinear ill-posed equations with monotone operators

Authors : S. George and M.T. Nair

Journal : J. Inverse and Ill-Posed Problems

Volume :25 Page: 543-551 DOI: DOI:10.1515/JIIP-2014-0049

Year: 2017

A discrete regularization method for Ill-posed operator equations,

Authors : M. T. Nair

Journal : The Journal of Analysis

Volume :25 Page: 53 - 266 DOI: DOI 10.1007/s41478-017-0047-4

Year: 2017

A note on some approximation theorems in measure theory

Authors : S. Kesavan and M.T. Nair

Journal : Mathematics Newsletter, Ramanujan Mathematical Society

Volume :27 Page: 170-174

Year: 2016

A note on compactness of unit ball in a normed linear space

Authors : M.T. Nair

Journal : Mathematics Newsletter, Ramanujan Mathematical Society

Volume :27 Page: 168-170

Year: 2016

Truncated Spectral Regularization for an Ill-Posed Nonhomogeneous Parabolic Problem

Authors : A. Jana and M.T. Nair

Journal : J. Math. Anal. Appl.

Volume :438 Page: 351-372.

Year: 2016

Compact operators and Hilbert scales in ill-posed problems

Authors : M.T. Nair

Journal : Mathematics Student

Volume :85 Page: 45-61

Year: 2016

Quasi-reversibility method for an ill-posed nonhomogeneous parabolic problem

Authors : A. Jana and M.T. Nair

Journal : Numer. Funct. Anal. Optim.

Volume :37 Page: 529–1550 DOI: dx.doi.org/10.1080/01630563.2016.1216448

Year: 2016

Morozov-type discrepancy principle for nonlinear ill-posed problems under η -condition

Authors : M.T. Nair

Journal : , Proc. Indian Acad. Sci. (Math. Sci)

Volume :125 Page: 227-238.

Year: 2015

A unified treatment for Tikhonov regularization using a general stabilizing operator

Authors : M.T. Nair

Journal : Analysis and Applications

Volume :13 Page: 201-215

Year: 2015

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