The spaces <mml:math alttext="$\theta _M $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>&#952;</mml:mi><mml:mi>M</mml:mi></mml:msub></mml:mrow></mml:math> and <mml:math alttext="$\theta '_C $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:msup><mml:mi>&#952;</mml:mi><mml:mo>&#8242;</mml:mo></mml:msup><mml:mi>C</mml:mi></mml:msub></mml:mrow></mml:math> of multiplication and convolution operators on temperate distributions, together with their strong duals <mml:math alttext="$\theta '_M $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:msup><mml:mi>&#952;</mml:mi><mml:mo>&#8242;</mml:mo></mml:msup><mml:mi>M</mml:mi></mml:msub></mml:mrow></mml:math> and <mml:math alttext="$\theta _C $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>&#952;</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:mrow></mml:math>, are Montel and distinguished.

A note on the spaces <mml:math alttext="$\theta _M $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>θ</mml:mi><mml:mi>M</mml:mi></mml:msub></mml:mrow></mml:math> and <mml:math alttext="$\theta '_M $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:msup><mml:mi>θ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mi>M</mml:mi></mml:msub></mml:mrow></mml:math>

A note on the spaces <svg style="vertical-align:-3.27605pt" height="16.3125" version="1.1" viewBox="0 0 21.362499 16.3125" width="21.362499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path id="x1D703" d="M475 507q0 -83 -20 -172t-56 -167.5t-93.5 -129t-125.5 -50.5q-157 0 -157 227q0 78 21.5 164t59 161t96.5 123.5t126 48.5q79 0 114 -58t35 -147zM391 522q0 155 -81 155q-62 0 -111 -82.5t-73 -200.5h253q12 81 12 128zM373 346h-255q-12 -91 -12 -150q0 -72 20 -123&#xA;t63 -51q34 0 64 28.5t52.5 77t39 103t28.5 115.5z" /></g><g transform="matrix(.012,-0,0,-.012,8.525,16.25)"><path id="x1D440" d="M998 650l-8 -28q-71 -4 -86 -16t-22 -69l-50 -397q-3 -28 -4.5 -44t2 -29t6.5 -18.5t17 -10.5t24.5 -6.5t37.5 -3.5l-8 -28h-271l7 28q63 6 78 22t25 90l60 415h-2l-353 -552h-23l-130 536h-2l-70 -254q-44 -158 -47 -188q-5 -38 9 -51t71 -18l-6 -28h-241l8 28&#xA;q45 4 67 18.5t35 45.5q16 38 74 233l52 173q24 79 11.5 98t-89.5 26l6 28h177l136 -508l337 508h172z" /></g></svg> and <svg style="vertical-align:-3.27605pt" height="21.7875" version="1.1" viewBox="0 0 25.512501 21.7875" width="25.512501" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,17.65)"><use xlink:href="#x1D703"/></g><g transform="matrix(.012,-0,0,-.012,8.525,9.488)"><path id="x2032" d="M227 744l-123 -338l-31 15l73 368q12 3 41.5 -8t36.5 -20z" /></g><g transform="matrix(.012,-0,0,-.012,12.687,21.725)"><use xlink:href="#x1D440"/></g></svg> 

International Journal of Mathematics and Mathematical Sciences

A note on the spaces θM and θ′M

Abstract

Copyright