Coincidence of Schur Multipliers of the Drury-Arveson Space (2009)
Bhattacharya, Angshuman, Bhattacharyya, Tirthankar
In a purely multi-variable setting (i.e., the issues discussed in this note are not interesting in the single variable operator theory setting), we show that the coincidence of two operator valued...
Complete Pick Positivity and Unitary Invariance (2009)
Bhattacharya, Angshuman, Bhattacharyya, Tirthankar
The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel $k_S(z,w) = (1 -...
A Learning Algorithm for Risk-Sensitive Cost (2008)
Basu, Arnab, Bhattacharyya, Tirthankar, Borkar, Vivek S
A linear function approximation-based reinforcement learning algorithm is proposed for Markov decision processes with infinite horizon risk-sensitive cost. Its convergence is proved using the "o.d.e....
Contractive and Completely Contractive Homomorphisms of Planar Algebras (2005)
Bhattacharyya, Tirthankar, Misra, Gadadhar
We consider contractive homomorphisms of a planar algebra $A(\Omega)$ over a nitely connected bounded domain $\Omega \subseteq C$ and ask if they are necessarily completely contractive. We show that...
Characteristic Function of a Pure Commuting Contractive Tuple (2005)
Bhattacharyya, Tirthankar, Eschmeier, Joerg, Sarkar, Jaydeb
A theorem of Sz.-Nagy and Foias [9] shows that the characteristic function $\theta_T(z) = −T + zD_{T^*}(1_H - zT^*)^{-1}D_T$ of a completely non-unitary contraction T is a complete unitary...
Contractive and completely contractive maps over planar algebras (2005)
Bhattacharyya, Tirthankar, Misra, Gadadhar
We consider contractive homomorphisms of a planar algebra ${\mathcal A}(\Omega)$ over a finitely connected bounded domain $\Omega \subseteq \C$ and ask if they are necessarily completely contractive....
Characteristic Function of a Pure Commuting Contractive Tuple (2005)
Bhattacharyya, Tirthankar, Eschmeier, Joerg, Sarkar, Jaydeb
A theorem of Sz.-Nagy and Foias [9] shows that the characteristic function $\theta_T(z) = −T + zD_{T^*}(1_H - zT^*)^{-1}D_T$ of a completely non-unitary contraction T is a complete unitary...
Contractive and Completely Contractive Homomorphisms of Planar Algebras (2005)
Bhattacharyya, Tirthankar, Misra, Gadadhar
We consider contractive homomorphisms of a planar algebra $A(\Omega)$ over a nitely connected bounded domain $\Omega \subseteq C$ and ask if they are necessarily completely contractive. We show that...
Bhattacharyya, Tirthankar, Mohandas, JP
We Consider the two parameter Sturm Liouville system (1) $-y_{1}^{''} + q_{1} y_{1} = ( \lambda r_{11} + \mu r_{12}) y_{1} \mbox{ on } [0,1]$ with the boundary conditions $ \frac {y_{1}^{'} (0)...
Bhattacharyya, Tirthankar, Mohandas, JP
We Consider the two parameter Sturm Liouville system (1) $-y_{1}^{''} + q_{1} y_{1} = ( \lambda r_{11} + \mu r_{12}) y_{1} \mbox{ on } [0,1]$ with the boundary conditions $ \frac {y_{1}^{'} (0)...
Standard noncommuting and commuting dilations of commuting tuples (2003)
Bhat, Rajarama BV, Bhattacharyya, Tirthankar, Dey, Santanu
We introduce a notion called `maximal commuting piece' for tuples of Hilbert space operators. Given a commuting tuple of operators forming a row contraction, there are two commonly used dilations in...
Standard noncommuting and commuting dilations of commuting tuples (2003)
Bhat, Rajarama BV, Bhattacharyya, Tirthankar, Dey, Santanu
We introduce a notion called `maximal commuting piece' for tuples of Hilbert space operators. Given a commuting tuple of operators forming a row contraction, there are two commonly used dilations in...
Dilation of contractive tuples : a survey (2002)
This is a survey of dilation theory of contractive tuples starting from the unitary dilation of Sz.-Nagy and Foias to the present day state of maximality of the standard commuting dilation inside the...
Bhattacharyya, Tirthankar, Ko, Toma, Plestenjak, Bor
We study a system of ordinary differential equations linked by parameters and subject to boundary conditions depending on parameters. We assume certain definiteness conditions on the coefficient...
Standard noncommuting and commuting dilations of commuting tuples (2002)
Bhat, B. V. Rajarama, Bhattacharyya, Tirthankar, Dey, Santanu
We introduce a notion called `maximal commuting piece' for tuples of Hilbert space operators. Given a commuting tuple of operators forming a row contraction there are two commonly used dilations in...
Some thoughts on Ando’s theorem and Parrott’s example (2002)
Bagchi, Bhaskar, Bhattacharyya, Tirthankar, Misra, Gadadhar
In this short note, we present an elementary proof of Ando’s theorem within a restricted class P of homomorphisms modeled after Parrott’s example. We also show by explicit estimation that the...
Dilation of contractive tuples : a survey (2002)
This is a survey of dilation theory of contractive tuples starting from the unitary dilation of Sz.-Nagy and Foias to the present day state of maximality of the standard commuting dilation inside the...
Some thoughts on Ando’s theorem and Parrott’s example (2002)
Bagchi, Bhaskar, Bhattacharyya, Tirthankar, Misra, Gadadhar
In this short note, we present an elementary proof of Ando’s theorem within a restricted class P of homomorphisms modeled after Parrott’s example. We also show by explicit estimation that the...
A Model Theory For $q$-Commuting Contractive Tuples (2002)
Bhat, Rajarama BV, Bhattacharyya, Tirthankar
A contractive tuple is a tuple $(T_1, \ldots , T_d)$ of operators on a common Hilbert space such that $T_1T_1^* + \cdots + T_dT_d^* \leq 1$. It is said to be $q$-commuting if $T_jT_i = q_{ij}T_iT_j$...
Bhattacharyya, Tirthankar, Ko, Toma, Plestenjak, Bor
We study a system of ordinary differential equations linked by parameters and subject to boundary conditions depending on parameters. We assume certain definiteness conditions on the coefficient...
A Model Theory For $q$-Commuting Contractive Tuples (2002)
Bhat, Rajarama BV, Bhattacharyya, Tirthankar
A contractive tuple is a tuple $(T_1, \ldots , T_d)$ of operators on a common Hilbert space such that $T_1T_1^* + \cdots + T_dT_d^* \leq 1$. It is said to be $q$-commuting if $T_jT_i = q_{ij}T_iT_j$...