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Norms of Time-Domain Functions and Convolution Operators

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Abstract

This chapter develops various norms of time-domain functions and convolution operators to obtain bounds for transient system response. Besides the usual p-norm we can define another norm, the residue norm (or r-norm), based on the singularities in the complex-frequency (or Laplace-transform) plane.

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References

  1. C.E. Baum (1980), Electromagnetic topology: A formal approach to the analysis and design of complex electronic systems, Interaction Note 400, September 1980, and Proc. EMC Symposium, Zürich, March 1981, pp. 209–214.

    Google Scholar 

  2. C.E. Baum (1985), On the use of electromagnetic topology for the decomposition of scattering matrices for complex physical structures, Interaction Note 454, July 1985.

    Google Scholar 

  3. F.M. Tesche (1978), Topological concepts for internal EMP interaction, IEEE Trans. Antennas and Propagation, vol. 26, January 1978, pp. 60–64, and IEEE Trans. EMC, vol. 20, February 1978, pp. 60–64.

    Article  Google Scholar 

  4. A.K. Agrawal and C.E. Baum (1983), Bounding of signal levels at terminations of a multiconductor transmission-line network, Interaction Note 419, April 1983, and Electromagnetics, vol. 8, 1988, pp. 375–422.

    Google Scholar 

  5. F.C. Yang and C.E. Baum (1983), Use of matrix norms of interaction super-matrix blocks for specifying electromagnetic performance of subshields, Interaction Note 427, April 1983, also as (same authors), Electromagnetic topology: Measurements and norms of scattering parameters of subshields, Electromagnetics, vol. 6, 1986, pp. 47–72.

    Google Scholar 

  6. C.E. Baum, Bounds on norms of scattering matrices, Interaction Note 432, June 1983, and Electromagnetics, vol. 6, 1986, pp. 33–45.

    Google Scholar 

  7. C.E. Baum (1983), Black box bounds, Interaction Note 429, May 1983, and Proc. EMC Symposium, Zürich, March 1985, pp. 381–386.

    Google Scholar 

  8. C.E. Baum (1984), Some bounds concerning the response of linear systems with a nonlinear element, Interaction Note 438, June 1984.

    Google Scholar 

  9. C.E. Baum (1979), Norms and Eigenvector Norms, Mathematics Note 63, November 1979.

    Google Scholar 

  10. I. Stakgold (1979), Green’s Functions and Boundary Value Problems, Wiley, New York.

    MATH  Google Scholar 

  11. C.-T. Chen (1984), Linear System Theory and Design, Holt, Rinehart, and Winston, New York.

    Google Scholar 

  12. C.E. Baum (1978), Toward an engineering theory of electromagnetic scattering: The singularity and eigenmode expansion methods, in Electromagnetic Scattering, P.L.E. Uslenghi, Academic Press, New York.

    Google Scholar 

  13. M. Abramowitz and I.A. Stegun (1964), Handbook of Mathematical Functions, AMS 55, National Bureau of Standards, Washington, D.C.

    MATH  Google Scholar 

  14. F. Riesz and B. Sz-Nagy (1955), Functional Analysis, Frederick Ungar, New York.

    Google Scholar 

  15. V.I. Krylov (1962), Approximate Calculation of Integrals, Macmillan, London.

    MATH  Google Scholar 

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© 1990 Springer-Verlag New York, Inc.

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Baum, C.E. (1990). Norms of Time-Domain Functions and Convolution Operators. In: Kritikos, H.N., Jaggard, D.L. (eds) Recent Advances in Electromagnetic Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3330-5_2

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  • DOI: https://doi.org/10.1007/978-1-4612-3330-5_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7969-3

  • Online ISBN: 978-1-4612-3330-5

  • eBook Packages: Springer Book Archive

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