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Guido Weiss

Guido Weiss is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Guido Weiss rather than just read about it. In short: Guido Leopold Weiss (29 December 1928–25 December 2021 in St. Louis) was an American mathematician, working in analysis, especially Fourier analysis and harmonic analysis.

Guido Weiss — main illustration
Guido Weiss — illustration

Key takeaways

  • Guido Weiss belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Guido Weiss to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Guido Weiss from memory before moving on to harder problems.

Reference excerpt

Guido Leopold Weiss (29 December 1928–25 December 2021 in St. Louis) was an American mathematician, working in analysis, especially Fourier analysis and harmonic analysis.

Childhood Weiss was born in Trieste Italy into a Jewish family. His parents, Edoardo and Vonda Weiss, were both psychiatrists. Weiss was forced out of school at the age of 9, upon the passage of Italy's Italian Racial Laws, which forbade all Jewish children from attending public school. He attended a Jewish school in Rome until the end of 1939 when his father was sponsored by members of the Menninger family to emigrate to America. The family settled in Topeka, Kansas.

Career Weiss studied at the University of Chicago, where he received in 1951 his master's degree and in 1956 under Antoni Zygmund his PhD with thesis On certain classes of function spaces and on the interpolation of sublinear operators. At DePaul University he became an instructor in 1955, an assistant professor in 1956, and in 1959 an associate professor. in 1960 he was a visiting professor in Buenos Aires and in the same year a postdoc at the Institut Henri Poincaré in Paris. In 1961 Weiss became an associate professor and in 1963 a professor at Washington University in St. Louis, where from 1967 to 1970 he was also chair of the mathematics department. He was a visiting professor at several universities, including the University of Geneva (1964–65), the Université Paris-Sud (1970–71), the Scuola Normale Superiore in Pisa (1980), in Madrid and in Beijing. In the academic year 1987–88 he was at MSRI as the organizer of a program in classical analysis. In 1967 Weiss won the Chauvenet Prize for his article Harmonic Analysis. In 1994 he was given honorary doctorates in Milan and Barcelona. In 2012 he became a fellow of the American Mathematical Society.

Works Harmonic Analysis. In: Studies in Real and Complex Analysis, edited by I. I. Hirschman. MAA Studies in Mathematics, Vol. 3, Mathematical Association of America, Washington, DC, 1965, pp. 124–178. with Elias Stein: Introduction to Fourier Analysis on Euclidean spaces. Princeton University Press 1971. with Ronald Coifman: Analyse harmonique non-commutative sur certains espaces homogènes. É́tude de certaines intégrales singulières. Springer-Verlag 1971. 2006 pbk edition with Ronald Coifman: Transference methods in analysis. AMS 1977. with Eugenio Hernandez: A first course on Wavelets. Boca Raton, CRC Press 1996. with Michael Frazier, Björn Jawerth: Littlewood–Paley theory and the study of function spaces. AMS 1991. with William Boothby (eds.): Symmetric spaces. Dekker 1972.

References

External links Homepage in St. Louis Special Issue Celebrating Guido L. Weiss for his Ninetieth Birthday

Illustrations

Guido Weiss illustration

Worked examples

Example 1 — a first encounter with Guido Weiss

Start with the simplest possible case. Write down what Guido Weiss claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Guido Weiss before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Guido Weiss ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Guido Weiss

In research
Guido Weiss appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Guido Weiss in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Guido Weiss is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1928 births, 2021 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Guido Weiss outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Guido Weiss in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Guido Weiss means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Guido Weiss out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Guido Weiss in simple terms?

Guido Leopold Weiss (29 December 1928–25 December 2021 in St. Louis) was an American mathematician, working in analysis, especially Fourier analysis and harmonic analysis.

Why does Guido Weiss matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Guido Weiss?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Guido Weiss.

Tags

  • 1928 births
  • 2021 deaths
  • 20th-century American mathematicians
  • 21st-century American mathematicians
  • DePaul University faculty
  • Fellows of the American Mathematical Society
  • Italian emigrants to the United States
  • People from Trieste
  • University of Chicago alumni
  • Washington University in St. Louis mathematicians

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