https://dspace.iiti.ac.in:8080/jspui/handle/123456789/9541 2026-06-26T21:04:45Z 2026-06-26T21:04:45Z Agarwal, Archit https://dspace.iiti.ac.in:8080/jspui/handle/123456789/18452 2026-06-22T10:52:47Z 2026-04-16T00:00:00Z

Title: Ramanujan’s five entries, weighted partition identities and divisor generating q-series with applications to probability theory and random graphs Authors: Agarwal, Archit Abstract: Ramanujan recorded many q-series identities in his notebooks and lost notebook. At the end of his second notebook, he mentioned five q-series identities. In 2021, Dixit and Maji obtained a q-series identity that enabled them to derive three of five Ramanujan’s q-series identities. Later, a unified generalization of these five q-series identities was obtained by Bhoria, Eyyunni and Maji and a finite analogue of this generalization was subsequently established by Dixit and Patel, yielding finite analogues of all five identities of Ramanujan. One of the primary objectives of this thesis is to develop a one variable generalization of the aforementioned identity of Bhoria et. al., together with its finite analogue, thereby extending the work of Dixit and Patel. As a consequence, we derive one variable generalizations of each of Ramanujan’s five identities along with their corresponding finite analogues.

2026-04-16T00:00:00Z Wankhede, Sheetal Sanjay https://dspace.iiti.ac.in:8080/jspui/handle/123456789/18104 2026-04-16T06:04:42Z 2026-04-08T00:00:00Z

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 Sahil https://dspace.iiti.ac.in:8080/jspui/handle/123456789/18094 2026-04-15T06:50:44Z 2026-03-10T00:00:00Z

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 Navneet https://dspace.iiti.ac.in:8080/jspui/handle/123456789/17745 2026-03-27T11:34:55Z 2026-03-10T00:00:00Z

Title: Characterization and explicit construction of pairwise orthogonal parseval frames on LCA groups Authors: Navneet

2026-03-10T00:00:00Z