What Do You Know About Herz Schur Multipliers?

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  • 1/10 Questions

    Which is another term that can be used to describe weak topology? 

    • Initial topology
    • Final topology
    • Basic topology
    • Fixed topology
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About This Quiz

Herz–Schur multipliers were named after two scientists: Carl S. Herz and Issai Schur. The multiplier was introduced by Haagerup and collaborators in 1985 and it is a special kind of mapping used in the field of representation theory, from a group to the complex number field. This quiz will help you know a bit more about Herz–Schur multipliers and if you already know, you can still try it out.

What Do You Know About Herz Schur Multipliers? - Quiz

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  • 2. 
    What is the S in Carl S. Herz?  - ProProfs

    What is the S in Carl S. Herz? 

    • Stanley

    • Samuel

    • Seth

    • Scott

    Correct Answer
    A. Samuel
    Explanation
    The S in Carl S. Herz stands for Samuel.

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  • 3. 
    Which of these is not a category of Herz-Schur multipliers?  - ProProfs

    Which of these is not a category of Herz-Schur multipliers? 

    • Positive multipliers

    • Idempotent multipliers

    • Radial multipliers

    • Negative multipliers

    Correct Answer
    A. Negative multipliers
    Explanation
    The question asks for a category of Herz-Schur multipliers that is not included in the given options. The options provided include positive multipliers, idempotent multipliers, radial multipliers, and negative multipliers. Out of these options, the correct answer is "Negative multipliers," as it is the only option that is not a category of Herz-Schur multipliers.

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  • 4. 
    Under what are the multipliers categorized?  - ProProfs

    Under what are the multipliers categorized? 

    • Systematic analysis

    • Dirichlet analysis

    • Transformational analysis

    • Harmonic analysis

    Correct Answer
    A. Harmonic analysis
    Explanation
    The multipliers are categorized under harmonic analysis. Harmonic analysis is a branch of mathematics that deals with the representation of functions or signals as the superposition of basic waves. It involves the study of the properties and behavior of harmonic functions, Fourier series, and Fourier transforms. Multipliers, in this context, refer to functions that act on the Fourier coefficients of a function, modifying or transforming them in some way. Therefore, harmonic analysis is the appropriate category for the study of multipliers.

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  • 5. 
    The existence of a semi-group of Herz-Schur multipliers generated by a proper function is equivalent to which property?  - ProProfs

    The existence of a semi-group of Herz-Schur multipliers generated by a proper function is equivalent to which property? 

    • Schur's property

    • Herz multipliers

    • Haagerup property

    • Linearly bounded function

    Correct Answer
    A. Haagerup property
    Explanation
    The existence of a semi-group of Herz-Schur multipliers generated by a proper function is equivalent to the Haagerup property.

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  • 6. 
    Which of the following is another topology? - ProProfs

    Which of the following is another topology?

    • Tough topology

    • Great topology

    • Strong topology

    • Dual topology

    Correct Answer
    A. Strong topology
    Explanation
    The correct answer is "Strong topology". This is because "Strong topology" is listed as one of the options for another topology. The other options, "Tough topology", "Great topology", and "Dual topology", are not listed as possible answers.

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  • 7. 
    What happens if the conditions of Haagerup's theorem are fulfilled? - ProProfs

    What happens if the conditions of Haagerup's theorem are fulfilled?

    • ||u||cbm = u(e)

    • ||u||cbt = u(e)

    • ||u||cbm = u(f)

    • ||u||cbn = u(e)

    Correct Answer
    A. ||u||cbm = u(e)
    Explanation
    If the conditions of Haagerup's theorem are fulfilled, it means that the norm of the completely bounded multiplier (||u||cbm) is equal to the value of u at the identity element of the group (u(e)).

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  • 8. 
    The set of all Idempotent Herz-Schur multipliers is what type of algebra? - ProProfs

    The set of all Idempotent Herz-Schur multipliers is what type of algebra?

    • Quadratic algebra

    • Boolean algebra

    • Schur's algebra

    • Negative algebra

    Correct Answer
    A. Boolean algebra
    Explanation
    The set of all Idempotent Herz-Schur multipliers is a type of algebra known as Boolean algebra. Boolean algebra is a mathematical structure that deals with binary variables and logical operations such as AND, OR, and NOT. It is named after mathematician George Boole and is widely used in computer science and digital electronics for designing and analyzing logic circuits. In Boolean algebra, the concept of idempotence is important as it refers to an operation that, when applied multiple times, produces the same result as if it were applied only once.

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  • 9. 
    A Herz-Schur multiplier is a group of what? - ProProfs

    A Herz-Schur multiplier is a group of what?

    • Arithmetic theory

    • Marginal theory

    • Representational theory

    • Convolution

    Correct Answer
    A. Representational theory
    Explanation
    A Herz-Schur multiplier is a group that belongs to the field of representational theory. This theory focuses on studying the different ways in which groups can be represented or expressed through mathematical structures. The Herz-Schur multiplier specifically deals with the representation of groups in terms of their multipliers, which are certain types of functions that provide information about the group's structure and properties. Therefore, the correct answer is representational theory.

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  • 10. 
    Haagerup was introduced together with another scientist. Which of these is the scientist? - ProProfs

    Haagerup was introduced together with another scientist. Which of these is the scientist?

    • P. Austin

    • L. Schur

    • J. Kraus

    • H. Henry

    Correct Answer
    A. J. Kraus
    Explanation
    The correct answer is J. Kraus because the question states that Haagerup was introduced together with another scientist. Therefore, J. Kraus must be the scientist who was introduced with Haagerup.

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  • Mar 18, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Jul 19, 2018
    Quiz Created by
    AdeKoju
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