Where Can I Find an Accessible Introduction to Hyperfunctions?

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SUMMARY

This discussion focuses on the search for accessible resources on hyperfunctions, particularly for individuals with engineering backgrounds. Francesco expresses difficulty in finding suitable introductory materials, citing expensive textbooks like Kaneko's "Introduction to the Theory of Hyperfunctions" and Imai's "Applied Hyperfunction Theory," which is currently out of stock. The conversation highlights the technical nature of existing literature, with suggestions that most resources are too advanced for beginners.

PREREQUISITES
  • Basic understanding of mathematical concepts related to integrals
  • Familiarity with advanced calculus
  • Knowledge of functional analysis
  • Interest in mathematical physics
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  • Research accessible online tutorials on hyperfunctions
  • Explore introductory courses in functional analysis
  • Look for lecture notes or video series on hyperfunctions
  • Investigate alternative mathematical topics that align with engineering applications
USEFUL FOR

Engineers, mathematicians, and students seeking to understand hyperfunctions and their applications in mathematical physics, particularly those looking for beginner-friendly resources.

Coelum
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Dear all,
I read about hyperfunctions in Penrose's masterpiece "Road to Reality" and I just met them again (in disguise) in a set of notes on "tricks on computing definite real integrals". Being an engineer with a curiosity for math, I would like to understand a bit more, so I am looking for a tutorial or an introduction to hyperfunctions, possibly with exercises. So far I found only costly or out-of-stock textbooks (like Kaneko's "Introduction to the Theory of Hyperfunctions" - 175$ ! - or Imai's "Applied Hyperfunction Theory" - out of stocks). I also found the original Sato's articles (from Wikipedia), but they are too technical and dry for my background. Any hint?
Thanks,

Francesco
 
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Unfortunately, seeing as most of the theory has only been developed in the last 50 years, you can bet that most treatments of the topic will have about that (high) level of technicality. Imai's book would be the least technical and is designed for physicists/engineers, but is quite hard to find. You might just have to find another mathematical curiosity to pursue.
 

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