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Quantitative Analysis
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
1. Calculational Linear Algebra.
2. Wavelet Analysis.
A. Elementary definitions of wavelet analysis.
B. Haar functions.
C. Multiresolution analysis.
D. Orthonormal wavelet bases.
E. Discrete wavelet transform.
F. Construction of MRA from scaling filter or auxiliary function.
a. Quadrature mirror filter (QMF) conditions.
b. Recovering scaling function from auxiliary function. Cascade algorithm.
c. Recovering MRA from auxiliary function.
G. Consequences and conditions for vanishing moments of wavelets.
H. Existence of smooth compactly supported wavelets. Daubechies polynomials.
I. Semi-orthogonal wavelet bases.
J. Construction of (G)MRA and wavelets on an interval.
3. Finite element method.
4. Construction of approximation spaces.
5. Time discretization.
6. Variational inequalities.
VIII. Bibliography
Notation. Index. Contents.

Construction of MRA from scaling filter or auxiliary function.


ne procedure for construction of an MRA was already presented in the section ( Construction of MRA ). The procedure in that section assumes existence of a function $\phi$ that must possess some restrictive and obscure properties.

In this section we pursue construction of a scaling function $\phi$ from a function $m_{0}$ with directly verifiable properties.




a. Quadrature mirror filter (QMF) conditions.
b. Recovering scaling function from auxiliary function. Cascade algorithm.
c. Recovering MRA from auxiliary function.

Notation. Index. Contents.


















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