eBook ISBN:  9780821875933 
Product Code:  CONM/7.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821875933 
Product Code:  CONM/7.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 7; 1982; 109 ppMSC: Primary 41; Secondary 30; 44

Table of Contents

Chapters

1. Cardinal Spline Functions

2. A Complex Contour Integral Representation of Basis Spline Functions (Compact Paths)

3. The Case of Equidistant Knots

4. Cardinal Exponential Spline Functions and Interpolants

5. Inversion of Laplace Transform

6. A Complex Contour Integral Representation of Cardinal Exponential Spline Functions (NonCompact Paths)

7. A Complex Contour Integral Representation of EulerFrobenius Polynomials (NonCompact Paths)

8. Cardinal Exponential Spline Interpolants of Higher Order

9. Convergence Behaviour of Cardinal Exponential Spline Interpolants

10. Divergence Behaviour of Polynomial Interpolants on Compact Intervals (The MérayRunge Phenomenon)

11. Cardinal Logarithmic Spline Interpolants

12. Inversion of Mellin Transform

13. A Complex Contour Integral Representation of Cardinal Logarithmic Spline Interpolants (NonCompact Paths)

14. Divergence Behaviour of Cardinal Logarithmic Spline Interpolants (The NewmanSchoenberg Phenomenon)

15. Summary and Concluding Remarks

References

Subject Index

Author Index


Reviews

This book contains a very comprehensive treatment of most of the author's original results in the theory of complex integral representation of cardinal spline functions. The basic idea of the book is to use a suitable inverse integral transform instead of the direct transform itself and then to have recourse to the methods of complex analysis applied to cardinal exponential splines and cardinal logarithmic splines. The method of complex contour integral representation yields a unified treatment of both cases. Besides presenting an outline of inverse integral transform technique, the book investigates several related topics. These include: (1)~various complex integral representations of the basis spline functions, (2)~a useful complex contour integral representation of the EulerFrobenius polynomials and its consequences, and (3)~the classical MérayRunge phenomenon. This approach to cardinal spline functions provides a very instructive illustration of the application of inverse integral transform techniques combined with complex variable methods to recent problems arising in approximation theory. Each section of the book ends with a few references and comments.
In the reviewer's opinion, this book will be very useful to a broad audience, interested in present developments of approximation theory.
Mathematical Reviews


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Chapters

1. Cardinal Spline Functions

2. A Complex Contour Integral Representation of Basis Spline Functions (Compact Paths)

3. The Case of Equidistant Knots

4. Cardinal Exponential Spline Functions and Interpolants

5. Inversion of Laplace Transform

6. A Complex Contour Integral Representation of Cardinal Exponential Spline Functions (NonCompact Paths)

7. A Complex Contour Integral Representation of EulerFrobenius Polynomials (NonCompact Paths)

8. Cardinal Exponential Spline Interpolants of Higher Order

9. Convergence Behaviour of Cardinal Exponential Spline Interpolants

10. Divergence Behaviour of Polynomial Interpolants on Compact Intervals (The MérayRunge Phenomenon)

11. Cardinal Logarithmic Spline Interpolants

12. Inversion of Mellin Transform

13. A Complex Contour Integral Representation of Cardinal Logarithmic Spline Interpolants (NonCompact Paths)

14. Divergence Behaviour of Cardinal Logarithmic Spline Interpolants (The NewmanSchoenberg Phenomenon)

15. Summary and Concluding Remarks

References

Subject Index

Author Index

This book contains a very comprehensive treatment of most of the author's original results in the theory of complex integral representation of cardinal spline functions. The basic idea of the book is to use a suitable inverse integral transform instead of the direct transform itself and then to have recourse to the methods of complex analysis applied to cardinal exponential splines and cardinal logarithmic splines. The method of complex contour integral representation yields a unified treatment of both cases. Besides presenting an outline of inverse integral transform technique, the book investigates several related topics. These include: (1)~various complex integral representations of the basis spline functions, (2)~a useful complex contour integral representation of the EulerFrobenius polynomials and its consequences, and (3)~the classical MérayRunge phenomenon. This approach to cardinal spline functions provides a very instructive illustration of the application of inverse integral transform techniques combined with complex variable methods to recent problems arising in approximation theory. Each section of the book ends with a few references and comments.
In the reviewer's opinion, this book will be very useful to a broad audience, interested in present developments of approximation theory.
Mathematical Reviews