https://dspace.iiti.ac.in:8080/jspui/handle/123456789/9541 2026-05-12T17:06:24Z https://dspace.iiti.ac.in:8080/jspui/handle/123456789/18104 Title: Univalent harmonic functions and their applications to special functions [RESTRICTED THESIS-03 Months] Authors: Wankhede, Sheetal Sanjay Abstract: [Abstract is restricted for 03 Months, due to IPR related issue] 2026-04-08T00:00:00Z https://dspace.iiti.ac.in:8080/jspui/handle/123456789/18094 Title: Convolutional frames for sampling, signal recovery and uncertainty principles Authors: Sahil Abstract: KEYWORDS: B-spline; Convolutional frame; Derivative sampling; Erasures; Fiberization map; Filter bank; Frame; Fusion frame; Locally compact group; Multi-channel sampling; Multiplication-invariant space; Periodic shiftinvariant space; Random sampling; Ramanujan filter bank; Ramanujan subspace; Ramanujan sums; Range function; Signal concentration; Supremum cosine angle; Tight frame; Translation-invariant space; Trigonometric polynomial; Twisted shift-invariant space; Uncertainty principle; Weyl-Zak transform; Zak transform. Sampling theory addresses the fundamental problem of determining whether a continuous function can be completely reconstructed from a discrete set of its values, commonly referred to as samples. The classical Shannon sampling theorem establishes that bandlimited functions are entirely determined by their values at integer points and can be reconstructed via sinc interpolation. Over the decades, this theory has been generalized to accommodate more realistic and flexible signal models, including nonuniform, derivative, multi-channel, and random sampling, as well as sampling in shift-invariant spaces. These developments have significantly broadened the scope of sampling theory, making it a unifying principle across communication, signal processing, medical imaging, geophysical sensing, machine learning, and quantum signal processing. 2026-03-10T00:00:00Z https://dspace.iiti.ac.in:8080/jspui/handle/123456789/17745 Title: Characterization and explicit construction of pairwise orthogonal parseval frames on LCA groups Authors: Navneet 2026-03-10T00:00:00Z https://dspace.iiti.ac.in:8080/jspui/handle/123456789/17499 Title: Sequential decision making under uncertainty: efficient Q-learning frameworks Authors: Shreyas SR Abstract: This thesis focuses on the development of efficient, convergent algorithms for solving problems in dynamic programming, reinforcement learning, and multi-agent learning. The work begins with novel first-order iterative schemes derived from a computationally expensive second-order method that approximates the Bellman equation using smooth functions. These new schemes retain the global convergence property while being more computationally efficient and easier to implement. Next, the thesis proposes a Weighted Smooth Q-Learning (WSQL) algorithm to address overestimation and underestimation biases in Q-learning and double Q-learning, respectively. By incorporating a weighted blend of mellowmax and log-sum-exp operators, WSQL achieves stability and theoretical convergence guarantees. The third part of the thesis introduces off-policy two-step Q-learning algorithms—both standard and smooth variants—that improve convergence and robustness without relying on importance sampling. Finally, the thesis extends these techniques to the multi-agent setting, proposing a multi-step minimax Q-learning algorithm for solving two-player zero-sum Markov games. Theoretical analysis ensures boundedness and almost sure convergence of the algorithms under suitable assumptions. Across all contributions, the proposed methods are validated through comprehensive numerical experiments on benchmark problems, demonstrating their e!ectiveness, robustness, and practical utility. Keywords: Reinforcement Learning, Q-learning, Bellman Equation, Value Iteration, Two-Player Zero-Sum Games, Stochastic Approximation, Smooth Operators. 2025-12-03T00:00:00Z