Z-Transform - ROC

Hi friends!

     I got a basic doubt in the theoritical dsp. Hope some one can
help me. My actual question is:

     Consider a sequence x(n) whose z-transform is X(z) and ROC is
characterized by Rx. Consider another sequence y(n) with z-transform
Y(z) and ROC Ry. Now
suppose that Rx and Ry are mutually exclusive that is their
intersection region is a null-set. Now if I define h(n) as convolution
of x(n) and y(n),

                          h(n)=x(n)*y(n)
Correspondingly:
                          H(z)=X(z)Y(z)

Now is it possible for H(z) to hav some region of convergence
eventhough the intersection of ROC's of X(z) and Y(z) is a null set?
If so please give one example to clear my doubt.

                                                   Thank u in advance,
                                                   Murty

sriram_friendly@yahoo.co.in (Murty) wrote in message news:<d906c40f.0308290030.33ae9fb5@posting.google.com>...
> Hi friends!
> 
>      I got a basic doubt in the theoritical dsp. Hope some one can
> help me. My actual question is:
> 
>      Consider a sequence x(n) whose z-transform is X(z) and ROC is
> characterized by Rx. Consider another sequence y(n) with z-transform
> Y(z) and ROC Ry. Now
> suppose that Rx and Ry are mutually exclusive that is their
> intersection region is a null-set. Now if I define h(n) as convolution
> of x(n) and y(n),
> 
>                           h(n)=x(n)*y(n)
> Correspondingly:
>                           H(z)=X(z)Y(z)
> 
> Now is it possible for H(z) to hav some region of convergence
> eventhough the intersection of ROC's of X(z) and Y(z) is a null set?
> If so please give one example to clear my doubt.
> 
>                                                    Thank u in advance,
>                                                    Murty

The ROC of the product of the two Z-transform contains the
intersection between ROC_x and ROC_y, and not is equal to the
intersection. The ROC of the product could be larger than the
intersection. If a pole that borders on the region of convergence of
one of the z-transform is canceled by a zero of the other, the ROC of
the product could be larger.
For the example i've to think about it. But i think that in literatury
there are a lot of them.