On minimizing the sum of squares of ℒ 2 norms of differential operators under constraints

Richard C. Brown; Allan M. Krall

Czechoslovak Mathematical Journal (1977)

  • Volume: 27, Issue: 1, page 132-143
  • ISSN: 0011-4642

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Brown, Richard C., and Krall, Allan M.. "On minimizing the sum of squares of $\mathcal {L}^2$ norms of differential operators under constraints." Czechoslovak Mathematical Journal 27.1 (1977): 132-143. <http://eudml.org/doc/12987>.

@article{Brown1977,
author = {Brown, Richard C., Krall, Allan M.},
journal = {Czechoslovak Mathematical Journal},
language = {eng},
number = {1},
pages = {132-143},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On minimizing the sum of squares of $\mathcal \{L\}^2$ norms of differential operators under constraints},
url = {http://eudml.org/doc/12987},
volume = {27},
year = {1977},
}

TY - JOUR
AU - Brown, Richard C.
AU - Krall, Allan M.
TI - On minimizing the sum of squares of $\mathcal {L}^2$ norms of differential operators under constraints
JO - Czechoslovak Mathematical Journal
PY - 1977
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 1
SP - 132
EP - 143
LA - eng
UR - http://eudml.org/doc/12987
ER -

References

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  1. L. D. Berkovitz, H. Pollard, 10.1007/BF00251656, Arch. Ratl. Mech. Anal. 38 (1970), 161-172. (1970) MR0270247DOI10.1007/BF00251656
  2. R. С. Brown, Duality theory for n -th order differential operators under Stieltjes boundary conditions, S.I.A.M. J. Math. Anal., to appear. Zbl0316.47027MR0385224
  3. R. C. Brown, Duality theory for n -th order differential operators under Stieltjes boundary conditions, II: Nonsmooth coefficients and nonsingular measures, Ann. Mat. Рurа. Appl., to appear. Zbl0316.47027MR0422745
  4. R. C. Brown, Adjoint domains and generalized splines, Czech. Math. J., 25 (1975), 134-147. (1975) Zbl0309.41014MR0397243
  5. N. Dunford, J. T. Schwartz, Linear operators, Part 1, Interscience, New York, 1975. (1975) 
  6. S. Goldberg, Unbounded linear operators, McGraw-Hill, New York, 1966. (1966) Zbl0148.12501MR0200692
  7. M. Golomb, J. Jerome, 10.1090/S0002-9947-1971-0269918-3, Trans. Amer. Math. Soc., 153 (1971), 235 - 264. (1971) Zbl0238.34027MR0269918DOI10.1090/S0002-9947-1971-0269918-3
  8. A. M. Krall, R. С Brown, n -th order differential systems under Stieltjes boundary conditions, MRC Tech. Summ. Rept. #1581. 
  9. D. G. Lunberger, Optimization by vector space methods, John Wiley, New York, 1969. (1969) MR0238472
  10. L. Schumaker, Spline functions: Theory and applications, in press. 

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