Department of Mathematics

Ashoka University is a private university located in Sonipat, Haryana, India, focusing on liberal arts and sciences. It was established in 2014.&nbsp;It is guided by an academic council of academics and scholars from around the world. The council sets the university&#39;s academic standard, advising on matters of curriculum, faculty hiring and research.&nbsp;

Ashoka University offers a full-time 3 (+ 1) year undergraduate programme. The University comprises of&nbsp;2500 plus students, with a mix of both national and international students.&nbsp; &nbsp;

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Ashoka University

In this paper, we prove a Szegö type limit theorem on ℓ 2 (Z d ). We take the self-adjoint operator H= - Δ + V on ℓ 2 (Z d ) , where (Δ u) (n) = ∑ | n - k | = 1 (u(k) - u(n)) and the operator V is the multiplication by a positive sequence { V(n) , n∈ Z d } with V(n) → ∞ as | n| → ∞. We take the orthogonal projection π λ onto the subspace, in ℓ 2 (Z d ) , spanned by eigenfunctions of H with eigenvalues ≤ λ. Let B be a zeroth order self-adjoint pseudo-difference operator associated with symbol b∈ S 1 , , ∞ (T d × Z d ). We then show for “nice functions” f, that limλ→∞Tr(f(πλBπλ))Tr(πλ)=limλ→∞1(2π)d∑V(n)≤λ∫Tdf(b(x,n))dx∑V(n)≤λ1. © 2018, Springer Nature Switzerland AG.

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Journal of Pseudo-Differential Operators and Applications

Szegö limit theorem on the lattice

Letters in Mathematical Physics

Correction to: Matrix versions of the Hellinger distance (Letters in Mathematical Physics, (2019), 109, 8, (1777-1804), 10.1007/s11005-019-01156-0)

We prove majorization inequalities for different means of positive definite matrices. These include the Cartan mean (the Karcher mean), the log Euclidean mean, the Wasserstein mean and the power mean. © 2018 Elsevier Inc.

Linear Algebra and Its Applications

Inequalities for the Wasserstein mean of positive definite matrices

arXiv

Orthogonal polynomials associated with a continued fraction of Hirschhorn

We present several theorems on strict and strong convexity, and higher order differential formulae for sandwiched quasi-relative entropy (a parametrized version of the classical fidelity). These are crucial for establishing global linear convergence of the gradient projection algorithm for optimization problems for these functions. The case of the classical fidelity is of special interest for the multimarginal optimal transport problem (the n-coupling problem) for Gaussian measures. © 2018 World Scientific Publishing Company.

Reviews in Mathematical Physics

Strong convexity of sandwiched entropies and related optimization problems

Relative hyperbolicity of Free-by-cyclic extensions

Groups, Geometry, and Dynamics

Anosov structures on Margulis spacetimes

Geometriae Dedicata

The Pressure metric on the Margulis Multiverse

The vibrating string problem is the source of much mathematics and physics. This article describes Lagrange’s formulation of a discretised version of the problem and its solution. This is also the first instance of an eigenvalue problem. © 2017, Indian Academy of Sciences.

Resonance

Vibrations and eigenvalues