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Analysis (Kobayashi) Lab
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Research in harmonic analysis that measures the “quantities” a function has and examines how they change under operators.
AboutAbout the lab
Reading a function's properties from its “quantities.”
Prof. Kobayashi studies the properties of functions from the standpoint of harmonic analysis and real analysis.
By examining the various “quantities” a function has, one can read off properties such as boundedness, continuity, differentiability, and integrability.
The yardsticks for measuring these quantities are norms and the function spaces defined by norms.
In particular, using function spaces called modulation spaces as a starting point, Prof. Kobayashi studies pseudodifferential operators and operators related to partial differential equations.
Key terms
- Harmonic analysis
- A branch of analysis that studies complicated functions by breaking them down into simple, wave-like components.
- Function space
- A collection of functions that share a certain property. Norms are used to measure the “quantities” of the functions.
- Pseudodifferential operator
- An operator that generalizes differentiation and integration so that they can be handled together.
ResearchResearch themes
The lab clarifies the properties of functions by examining the various “quantities” they have. Another subject of study is how these quantities change when an operator is applied to a function.
*Illustrative imageMeasuring the “Quantities” of Functions
Properties of functions such as boundedness, continuity, differentiability, and integrability are examined through the “quantities” the functions have. Various norms, and function spaces defined by norms, are used to measure these quantities.
*Illustrative imageOperators Seen Through Modulation Spaces
Interested in the function spaces called modulation spaces, introduced around 1980 by H. Feichtinger of Austria, the lab studies pseudodifferential operators and operators related to partial differential equations from this standpoint.
MembersFaculty
- ProfessorMasaharu Kobayashi
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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: “Unknown Sound Spectrogram” Daniel Hilse / CC BY-SA 4.0 (cropped)
- Measuring the “Quantities” of Functions: “Newton Mess Iridescence” Dicklyon / CC BY-SA 4.0 (cropped)
- Operators Seen Through Modulation Spaces: “Heat Equation 1D BE Color” Gong Chen, Brandon Cloutier, Ning Li, Benson K. Muite and Paul Rigge with contributions from Sudarshan Balakrishnan, Andre Souza and Jeremy West / CC BY-SA 3.0 (cropped)
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