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Kinoshita Lab
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A mathematics lab studying hyperbolic equations and wavelets.
AboutAbout the lab
Unraveling waves and wavelets through mathematics.
Associate Professor Tamotu Kinoshita studies hyperbolic equations, wave equations, and wavelet analysis.
The lab belongs to the analysis group of the Degree Program in Mathematics, and its research areas are microlocal analysis, initial value problems for hyperbolic equations, and wavelets.
Recent papers deal with the construction of band-limited wavelets and the application of wavelet-like orthonormal bases to the two-dimensional Radon transform.
Key terms
- Wavelet
- A function used to represent a function or signal by separating it according to position and scale of detail.
- Hyperbolic equation
- A family of partial differential equations that describe the propagation of waves, including the wave equation.
- Microlocal analysis
- A method in analysis that studies the singularities of a function by separating them by position and direction.
- Well-posedness of initial value problems
- The property that a solution exists and is unique, and that small differences in the initial state do not change the result greatly.
ResearchResearch themes
In the field of analysis, the lab studies initial value problems for hyperbolic equations and wavelets. Its work ranges from the construction of wavelets to applications to the Radon transform and wave equations.
*Illustrative imageInitial value problems for hyperbolic equations
Alongside microlocal analysis, initial value problems for hyperbolic equations are listed as a research area. A talk was also given at a university salon on differential equations that describe oscillatory phenomena.
Construction of wavelets
The lab studies how to construct wavelets. A recent paper deals with the construction of band-limited wavelets with a dilation factor of 4.
*Illustrative imageApplications to the Radon transform and wave equations
A paper constructs wavelet-like orthonormal bases and applies them to the two-dimensional Radon transform. The lab also works on applying multidimensional wavelets to multidimensional wave equations.
MembersFaculty
- Associate ProfessorTamotu Kinoshita
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Wave propagation in the uniform medium with defects 1” Akucenko / CC BY-SA 4.0 (cropped)
- Initial value problems for hyperbolic equations: “Ripple-tank-parabolic-mirror” MikeRun / CC BY-SA 4.0 (cropped)
- Applications to the Radon transform and wave equations: “Radon transform example” Michal Odložilík / CC BY-SA 4.0 (cropped)
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