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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
Author
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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.
a. Auxiliary function of OST.
b. Scaling equation for wavelet.
c. Existence of orthonormal wavelet bases.
E. Discrete wavelet transform.
F. Construction of MRA from scaling filter or 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.

Scaling equation for wavelet.


roposition

(Scaling equation 2) Let MATH be an MRA (see the definition ( Multiresolution analysis )) with the scaling function $\phi$ and MATH is the sequence defined in the proposition ( Scaling equation ). Set MATH Then MATH

Proof

We calculate MATH and use the formula ( Property of scale and transport 6 ): MATH MATH





Notation. Index. Contents.


















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