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Table of Contents:

Chapter 1: Introduction
1.1 Background of the Study
1.2 Statement of the Problem
1.3 Objectives of the Study
1.4 Significance of the Study
1.5 Scope of the Study
1.6 Limitations of the Study

Chapter 2: Literature Review
2.1 Overview of Hilbert Spaces
2.2 Introduction to Wavelets
2.3 Previous Studies on Approximating Hilbert Spaces Functions
2.4 Theoretical Framework

Chapter 3: Research Methodology
3.1 Research Design
3.2 Data Collection Methods
3.3 Data Analysis Techniques
3.4 Sampling Techniques
3.5 Research Variables
3.6 Ethical Considerations

Chapter 4: Discussion of Findings
4.1 Analysis of Data
4.2 Interpretation of Results
4.3 Comparison with Previous Studies
4.4 Implications of Findings

Chapter 5: Conclusion and Summary
5.1 Summary of Findings
5.2 Conclusion
5.3 Recommendations for Future Research

Brief Overview:

The thesis on “Approximating Hilbert spaces functions using wavelets” aims to explore the use of wavelet analysis in approximating functions in Hilbert spaces. Hilbert spaces are infinite-dimensional vector spaces equipped with an inner product that allows for the representation of functions as a series of orthogonal basis functions. Wavelets, on the other hand, are mathematical functions that can be used to represent signals or functions with both time and frequency characteristics.

The research will begin with an introduction to the topic, including the background of the study and the objectives to be achieved. The literature review will provide a theoretical framework by discussing previous studies on both Hilbert spaces and wavelet analysis. The research methodology will outline the design, data collection methods, and analysis techniques to be used in the study.

The discussion of findings will include the analysis and interpretation of data collected, as well as a comparison with previous studies in the field. The conclusion and summary chapter will summarize the key findings, draw conclusions from the research, and provide recommendations for future studies in this area.

Overall, this thesis seeks to contribute to the understanding of how wavelets can be used to approximate functions in Hilbert spaces, providing insights that could have practical implications in various fields such as signal processing, image compression, and data analysis.

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