Minimum-Energy Multiwavelet Frame on the Interval <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.8905pt" id="M1" height="15.1511pt" version="1.1" viewBox="-0.0657574 -12.2606 36.2337 15.1511" width="36.2337pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g50-92" d="M297 -163V-131C189 -122 187 -119 187 -41V582C187 660 190 663 297 672V704H122V-163H297Z"/></g><g transform="matrix(.017,0,0,-0.017,6.143,0)"><path id="g50-49" d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"/></g><g transform="matrix(.017,0,0,-0.017,14.5,0)"><path id="g50-45" d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z"/></g><g transform="matrix(.017,0,0,-0.017,21.478,0)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g><g transform="matrix(.017,0,0,-0.017,29.835,0)"><path id="g50-94" d="M237 -163V704H62V672C170 663 172 660 172 582V-40C172 -118 170 -122 62 -131V-163H237Z"/></g></svg>

<div>Graphs of multiscaling function and left (right) boundary multiscaling functions and MEMWFI with dilation factor 2 and multiplicity 2.</div>

Mathematical Problems in Engineering

fig2

Figure 2

Figure 2: Minimum-Energy Multiwavelet Frame on the Interval <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.8905pt" id="M1" height="15.1511pt" version="1.1" viewBox="-0.0657574 -12.2606 36.2337 15.1511" width="36.2337pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g50-92" d="M297 -163V-131C189 -122 187 -119 187 -41V582C187 660 190 663 297 672V704H122V-163H297Z"/></g><g transform="matrix(.017,0,0,-0.017,6.143,0)"><path id="g50-49" d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"/></g><g transform="matrix(.017,0,0,-0.017,14.5,0)"><path id="g50-45" d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z"/></g><g transform="matrix(.017,0,0,-0.017,21.478,0)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g><g transform="matrix(.017,0,0,-0.017,29.835,0)"><path id="g50-94" d="M237 -163V704H62V672C170 663 172 660 172 582V-40C172 -118 170 -122 62 -131V-163H237Z"/></g></svg> 